This Week's Finds in Mathematical Physics (Week 283)
John Baez
November 10, 2009
This Week's Finds in Mathematical Physics (Week 283)
John Baez
We had a great AMS meeting this weekend at UCR, with far too many
interesting talks going on simultaneously. For example, there were
two sessions on math related to knot theory, one on operator algebras,
one on noncommutative geometry, and one on homotopy theory and higher
algebraic structures! If I could clone myself, I'd have gone to all of
them.
I'd like to discuss some of the talks, and maybe even point you to some
videos. But the videos aren't available yet, so for now I'll just
summarize my own talk on "Who Discovered the Icosahedron", and some
geometry related to that. I'll conclude with a puzzle.
But first - the astronomy pictures of the week!
Galaxies are beautiful things, and there are lots of ways to enjoy
them. Here's the Milky Way in visible light - a detailed panorama
created from over 3000 individual pictures, carefully calibrated to
show large dust clouds:
1) Axel Mellinger, All-sky Milky Way panorama 2.0,
http://home.arcor.de/axel.mellinger/
You can see even more structure in this infrared panorama of the Milky
Way, created by the Spitzer Space Telescope:
2) Astronomy Picture of the Day, GLIMPSE the Milky Way,
http://apod.nasa.gov/apod/ap051216.html
The bright white splotches are star-forming regions. The greenish
wisps are hot interstellar gas. The red clouds are dust and organic
molecules like polycyclic aromatic hydrocarbons (see "week258"). The
darkest patches are regions of cool dust too thick for Spitzer to see
through.
But here's my favorite: the Andromeda Galaxy in viewed in ultraviolet
light:
3) Astronomy Picture of the Day, Ultraviolet Andromeda,
http://apod.nasa.gov/apod/ap090917.html
This was taken by Swift, NASA's ultraviolet satellite telescope.
At this frequency, young hot stars and dense star clusters dominate
the view. It's sort of ghostly looking, no?
Now for my talk on the early history of the icosahedron. This talk on
the early history of the icosahedron continues the tale begun in
"week236" and "week241". Someday it'll get folded into a paper on
special properties of the number 5, and 5-fold symmetry:
4) John Baez, Who discovered the icosahedron?, talk at the Special
Session on History and Philosophy of Mathematics, 2009 Fall Western
Section Meeting of the AMS, November 7, 2009.
Available at http://math.ucr.edu/home/baez/icosahedron/
The dodecahedron and icosahedron are the most exotic of the Platonic
solids, because they have 5-fold rotational symmetry - a possibility
that only exists for regular polytopes in 2, 3 or 4 dimensions. The
dodecahedron and icosahedron have the same symmetry group, because
they are Poincare duals: the vertices of one correspond to faces of
the other. But the icosahedron was probably discovered later. As
Benno Artmann wrote:
The original knowledge of the dodecahedron may have come from
crystals of pyrite, but in contrast the icosahedron is a pure
mathematical creation.... It is the first realization of an
entity that existed before only in abstract thought. (Well,
apart from the statues of gods!)
I'm not sure it's really anything close to the first "realization of
an entity that existed before only in abstract thought". But
it may have been the first "exceptional" object in mathematics -
roughtly speaking, an entity that doesn't fit into any easy pattern,
which is discovered as part of proving a classification theorem!
Other exceptional objects include the simple Lie group E8, and the
finite simple group M12. Intriguingly, many of these exceptional
objects" are related. For example, the icosahedron can be used to
construct both E8 and M12. But the first interesting classification
theorem was the classification of regular polyhedra: convex polyhedra
with equilateral polygons as faces, and the same number of faces
meeting at each vertex. This theorem appears almost at the end of
the last book of Euclid's Elements - Book XIII. It shows that the only
possibilities are the Platonic solids: the tetrahedron, the cube, the
octahedron, the dodecahedron and the icosahedron. And according to
traditional wisdom, the results in this book were proved by Theatetus,
who also discovered the icosahedron!
Indeed, Artmann cites an "an ancient note written in the margins of
the manuscript" of Book XIII, which says:
In this book, the 13th, are constructed the five so-called Platonic
figures which, however, do not belong to Plato, three of the five
being due to the Pythagoreans, namely the cube, the pyramid, and
the dodecahedron, while the octahedron and the icosahedron are due
to Theaetetus.
You may know Theaetetus through Plato's dialog of the same name, where
he's described as a mathematical genius. He's also mentioned in
Plato's dialogue called the Sophist. In the Republic, written around
380 BC, Plato complained that not enough is known about solid geometry:
... and for two reasons: in the first place, no government places
value on it; this leads to a lack of energy in the pursuit of it,
and it is difficult. In the second place, students cannot learn it
unless they have a teacher. But then a teacher can hardly be
found....
Theaetetus seems to have filled the gap: he worked on solid geometry
between 380 and 370 BC, perhaps inspired by Plato's interest in the
subject. He died from battle wounds and dysentery in 369 after Athens
fought a battle with Corinth.
But how certain are we that Theatetus discovered - or at least studied -
the icosahedron? The only hard evidence seems to be this "ancient
note" in the margins of the Elements. But who wrote it, and when?
First of all, if you hope to see an ancient manuscript by Euclid with
a scribbled note in the margin, prepare to be disappointed! All we
have are copies of copies of copies. The oldest remaining fragments
of the Elements date to centuries after Euclid's death: some from a
library in Herculaneum roasted by the eruption of Mount Vesuvius in 79
AD, a couple from the Fayum region near the Nile, and some from a
garbage dump in the Egyptian town of Oxyrhynchus.
There are various lines of copies of Euclid's Elements. Comparing
these to guess the contents of the *original* Elements is a difficult
and fascinating task. Unfortunately, in the fourth century AD, the
Greek mathematician Theon of Alexandria - Hypatia's dad - made a copy
that became extremely popular. So popular, in fact, that for many
centuries European scholars knew no line of copies that hadn't passed
through Theon! And Theon wasn't a faithful copyist: he added extra
propositions, lengthened some proofs, and omitted a few things too.
It seems he wanted to standardize the language and make it easier to
follow. This may have helped people trying to learn geometry -
but certainly not scholars trying to understand Euclid.
In 1808, Francois Peyrard made a marvelous discovery. He found that
the Vatican library had a copy of Euclid's Elements that hadn't
descended through Theon! This copy is now called "P". It dates back
to about 850 AD. I would love to know how Peyrard got his hands on it.
One imagines him rooting around in a dusty basement and opening a
trunk... but it seems that Napoleon somehow took this manuscript from
the Vatican to Paris.
In the 1880s, the great Danish scholar Johan Heiberg used "P" together
with various "Theonine" copies of the Elements to prepare what's still
considered the definitive Greek edition of this book. The
all-important English translation by Thomas Heath is based on this.
As far as I can tell, "P" is the only known non-Theonine copy of
Euclid except for the fragments I mentioned. Heath also used these
fragments to prepare his translation.
This is just a quick overview of a complicated detective story.
As always, the fractal texture of history reveals more complexity
the more closely you look.
Anyway, Heath thinks that Geminus of Rhodes wrote the "ancient note"
in the Elements crediting Theatetus. I'm not sure why Heath thinks
this, but Geminus of Rhodes was a Greek astronomer and mathematician
who worked during the 1st century BC.
In his charming article "The discovery of the regular solids", William
Waterhouse writes:
Once upon a time there was no problem in the history of the regular
solids. According to Proclus, the discoveries of Pythagoras
include "the construction of the cosmic solids," and early
historians could only assume that the subject sprang full-grown
from his head. But a better-developed picture of the growth
of Greek geometry made such an early date seem questionable, and
evidence was uncovered suggesting a different attribution. A
thorough study of the testimony was made by E. Sachs, and her
conclusion is now generally accepted: the attribution to Pythagoras
is a later misunderstanding and/or invention.
The history of the regular solids thus rests almost entirely on a
scholium to Euclid which reads as follows:
"In this book, the 13th, are constructed the 5 figures called
Platonic, which however do not belong to Plato. Three of these
5 figures, the cube, pyramid, and dodecahedron, belong to the
Pythagoreans; while the octahedron and icosahedron belong to
Theaetetus."
Theaetetus lived c. 415-369 B.C., so this version gives a
moderately late date; and it has the considerable advantage of
seeming unlikely. That is, the details in the scholium are not
the sort of history one would naively conjecture, and hence it
is probably not one of the stories invented in late antiquity.
As van der Waerden says, the scholium is now widely accepted
"precisely because [it] directly contradicts the tradition which
used to ascribe to Pythagoras anything that came along."
But probability arguments can cut both ways, and those scholars
who hesitate to accept the scholium do so primarily because it
seems too unlikely. There have been two main sticking places:
first, the earliness of the dodecahedron in comparison with the
icosahedron; and second, the surprising lateness of the octahedron.
The first objection, however, has been fairly well disposed of.
The mineral pyrite (FeS2) crystallizes most often in cubes and
almost-regular dodecahedra; it is quite widespread, being the most
common sulphide, and outstanding crystals are found at a number
of spots in Italy. Moreover it regularly occurs mixed with the
sulphide ores, and underlying the oxidized ores, of copper; these
deposits have been worked since earliest antiquity. Thus natural
dodecahedra were conspicuous, and in fact they did attract
attention: artificial dodecahedra have been found in Italy dating
from before 500 BC. Icosahedral crystals, in contrast, are much
less common. Hence there is no real difficulty in supposing that
early Pythagorean geometers in Italy were familiar with dodecahedra
but had not yet thought of the icosahedron.
Indeed, while I've heard that iron pyrite forms "pseudoicosahedra",
I've never seen one, while the "pyritohedra" resembling regular
dodecahedra are pretty common.
The puzzle of why the octahedron showed up so late seems to have this
answer: it was known earlier, but it was no big deal until the concept
of regular polyhedron was discovered! As Waterhouse says, the discovery
of the octahedron would be like the discovery of the 4rd perfect number.
Only the surrounding conceptual framework makes the discovery
meaningful.
So far, so good. But maybe the Greeks were not the first to discover
the icosahedron! In 2003, the famous mathematician Michael Atiyah and
the chemist Paul Sutcliffe wrote:
Although they are termed Platonic solids there is convincing
evidence that they were known to the Neolithic people of Scotland
at least a thousand years before Plato, as demonstrated by the stone
models pictured in Fig. 1 which date from this period and are kept
in the Ashmolean Museum in Oxford.
Various people including John McKay and myself spread this story without
examining it very critically. I did read Dorothy Marshall's excellent
paper "Carved stone balls", which catalogues 387 carved stone balls
found in Scotland, dating from the Late Neolithic to Early Bronze Age.
It has pictures showing a wide variety of interesting geometric
patterns carved on them, and maps showing where people have found
balls with various numbers of bumps on them. But it doesn't say
anything about Platonic solids.
In March of 2009, Lieven le Bruyn posted a skeptical investigation of
Atiyah and Sutcliffe's claim. For starters, he looked hard at the
photo in their paper:
... where's the icosahedron? The fourth ball sure looks like one
but only because someone added ribbons, connecting the centers of
the different knobs. If this ribbon-figure is an icosahedron, the
ball itself should be another dodecahedron and the ribbons illustrate
the fact that icosa- and dodecahedron are dual polyhedra. Similarly
for the last ball, if the ribbon-figure is an octahedron, the ball
itself should be another cube, having exactly 6 knobs. Who did adorn
these artifacts with ribbons, thereby multiplying the number of
"found" regular solids by two (the tetrahedron is self-dual)?
Who put on the ribbons? Lieven le Bruyn traced back the photo to
Robert Lawlor's 1982 book Sacred Geometry. In this book, Lawlor wrote:
The five regular polyhedra or Platonic solids were known and
worked with well before Plato's time. Keith Critchlow in his
book Time Stands Still presents convincing evidence that they
were known to the Neolithic peoples of Britain at least 1000
years before Plato. This is founded on the existence of a number
of spherical stones kept in the Ashmolean Museum at Oxford.
Of a size one can carry in the hand, these stones were carved into
the precise geometric spherical versions of the cube, tetrahedron,
octahedron, icosahedron and dodecahedron, as well as some additional
compound and semi-regular solids...
But is this really true? Le Bruyn discovered that the Ashmolean owns
only 5 Scottish stone balls - and their webpage shows a photo of them,
which looks quite different than the photo in Lawlor's book! They
have no ribbons on them. More importantly, they're different shapes!
The Ashmolean lists their 5 balls as having 7, 6, 6, 4 and 14
knobs, respectively - nothing like an icosahedron.
And here is where I did a little research of my own. The library at
UC Riverside has a copy of Keith Critchlow's 1979 book Time Stands
Still. In this book, we see the same photo of stones with ribbons
that appears in Lawlor's book - the photo that Atiyah and Suttcliffe
use. In Critchlow's book, these stones are called "a full set of
Neolithic 'Platonic solids'". He says they were photographed by one
Graham Challifour - but he gives no information as to where they came
from!
And Critchlow explicitly denies that the Ashmolean has an icosahedral
stone! He writes:
... the author has, during the day, handled five of these
remarkable objects in the Ashmolean museum.... I was rapt
in admiration as I turned over these remarkable stone objects
when another was handed to me which I took to be an icosahedron....
On careful scrutiny, after establishing apparent fivefold symmetry
on a number of the axes, a count-up of the projections revealed 14!
So it was not an icosahedron.
It seems the myth of Scottish balls shaped like Platonic solids
gradually grew with each telling. Could there be any truth to it?
Dorothy Marshall records Scottish stone balls with various numbers
of knobs, from 3 to 135 - but just two with 20, one at the National
Museum in Edinburgh, and one at the Kelvingrove Art Gallery and Museum
in Glasgow. Do these look like icosahedra? I'd like to know. But
even if they do, should we credit Scots with "discovering the
icosahedron"? Perhaps not.
So, it seems the ball is in Theaetetus' court.
Here are some references:
The quote from Benno Artmann appeared in a copy of the AMS Bulletin
where the cover illustrates a construction of the icosahedron:
5) Benno Artmann, About the cover: the mathematical conquest of
the third dimension, Bulletin of the AMS, 43 (2006), 231-235.
Also available at
http://www.ams.org/bull/2006-43-02/S0273-0979-06-01111-6/
For more, try this wonderfully entertaining book:
6) Benno Artmann, Euclid - The Creation of Mathematics, Springer,
New York, 2nd ed., 2001. (The material on the icosahedron is not
in the first edition.)
It's not a scholarly tome: instead, it's a fun and intelligent
introduction to Euclid's Elements with lots of interesting digressions.
A great book for anyone interested in math!
I should also get ahold of this someday:
7) Benno Artmann, Antike Darstellungen des Ikosaeders, Mitt. DMV 13
(2005), 45-50.
Heath's translation of and commentary on Euclid's Elements is available
online thanks to the Perseus Project. The scholium crediting Theatetus
for the octahedron and icosahedron is discussed here:
8) Euclid, Elements, trans. Thomas L. Heath, Book XIII,
Historical Note, p. 438. Also available at
http://old.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.01.0086&query=head%3D%23566
while the textual history of the Elements is discussed here:
9) Euclid, Elements, trans. Thomas L. Heath, Chapter 5: The Text,
p. 46. Also available at
http://old.perseus.tufts.edu/cgi-bin/ptext?lookup=Euc.+5
Anyone interested in Greek mathematics also needs these books by
Heath, now available cheap from Dover:
10) Thomas L. Heath, A History of Greek Mathematics. Vol. 1: From
Thales to Euclid. Vol. 2: From Aristarchus to Diophantus.
Dover Publications, 1981.
The long quote by Waterhouse comes from here:
11) William C. Waterhouse, The discovery of the regular solids,
Arch. Hist. Exact Sci. 9 (1972-1973), 212-221.
I haven't yet gotten my hold on this "thorough study" mentioned by
Waterhouse - but I will soon:
12) Eva Sachs, Die funf platonischen Koerper, zur Geschichte der
Mathematik und der Elementenlehre Platons und der Pythagoreer,
Berlin, Weidmann, 1917.
I also want to find this discussion of how Peyrard got ahold of the
non-Theonine copy of Euclid's Elements:
13) N. M. Swerlow, The Recovery of the exact sciences of antiquity:
mathematics, astronomy, geography, in Rome Reborn: The Vatican
Library and Renaissance Culture, ed. Grafton, 1993.
Here is Atiyah and Sutcliffe's paper claiming that the Ashmolean
has Scottish stone balls shaped like Platonic solids:
14) Michael Atiyah and Paul Sutcliffe, Polyhedra in physics,
chemistry and geometry, available as math-ph/0303071.
Here is le Bruyn's critical examination of that claim:
15) Lieven le Bruyn, The Scottish solids hoax, March 25, 2009,
http://www.neverendingbooks.org/index.php/the-scottish-solids-hoax.html
Here are the books by Critchlow and Lawlor -speculative books from
the "sacred geometry" tradition:
16) Keith Critchlow, Time Stands Still, Gordon Fraser, London, 1979.
17) Robert Lawlor, Sacred Geometry: Philosophy and Practice,
Thames and Hudson, London, 1982. Available at
http://www.scribd.com/doc/13155707/robert-lawlor-sacred-geometry-philosophy-and-practice-1982
Here's the Ashmolean website:
18) British Archaeology at the Ashmolean Museum, Highlights of the
British collections: stone balls,
http://ashweb2.ashmus.ox.ac.uk/ash/britarch/highlights/stone-balls.html
and here's Dorothy Marshall's paper on stone balls:
19) Dorothy N. Marshall, Carved stone balls, Proc. Soc. Antiq. Scotland,
108 (1976/77), 40-72. Available at
http://www.tarbat-discovery.co.uk/Learning%20Files/Carved%20stone%20balls.pdf
Finally, a bit of math.
In the process of researching my talk, I learned a lot about Euclid's
Elements, where the construction of the icosahedron - supposedly due to
Theaetetus - is described. This construction is Proposition XIII.16,
in the final book of the Elements, which is largely about the Platonic
solids. This book also has some fascinating results about the golden
ratio and polygons with 5-fold symmetry!
The coolest one is Proposition XIII.10. It goes like this.
Take a circle and inscribe a regular pentagon, a regular hexagon, and
a regular decagon. Take the edges of these shapes, and use them as the
sides of a triangle. Then this is a right triangle!
In other words, if
P
is the side of the pentagon,
H
is the side of the hexagon, and
D
is the side of the decagon, then
P^2 = H^2 + D^2
We can prove this using algebra - but Euclid gave a much cooler proof,
which actually find this right triangle hiding inside an icosahedron.
First let's give a completely uninspired algebraic proof.
Start with a unit circle. If we inscribe a regular hexagon in it,
then obviously
H = 1
So we just need to compute P and D. If we think of the unit circle as
living in the complex plane, then the solutions of
z^5 = 1
are the corners of a regular pentagon. So let's solve this equation.
We've got
0 = z^5 - 1 = (z - 1)(z^4 + z^3 + z^2 + z + 1)
so ignoring the dull solution z = 1, we must solve
z^4 + z^3 + z^2 + z + 1 = 0
This says that the center of mass of the pentagon's corners lies right
in the middle of the pentagon.
Now, quartic equations can always be solved using radicals, but it's
a lot of work. Luckily, we can solve this one by repeatedly using
the quadratic equation! And that's why the Greeks could construct
the regular pentagon using a ruler and compass.
The trick is to rewrite our equation like this:
z^2 + z + 1 + z^{-1} + z^{-2} = 0
and then like this:
(z + z^{-1})^2 + (z + z^{-1}) - 1 = 0
Now it's a quadratic equation in a new variable. So while I said this
proof would be uninspired, it did require a tiny glimmer of inspiration.
But that's all! Let's write
z + z^{-1} = x
so our equation becomes
x^2 + x - 1 = 0
Solving this, we get two solutions. The one I like is the golden
ratio:
x = phi = (-1 + sqrt(5))/2 ~ 0.6180339...
Next we need to solve
z + z^{-1} = phi
This is another quadratic equation:
z^2 - phi z + 1 = 0
with two conjugate solutions, one being
z = (phi + sqrt(phi^2 - 4))/2
I've sneakily chosen the solution that's my favorite 5th root of unity:
z = exp(2 pi i / 5) = cos(2pi/5) + i sin(2pi/5)
So, we're getting
cos(2pi/5) = phi/2
A fact we should have learned in high school, but probably never did.
Now we're ready to compute P, the length of the side of a pentagon
inscribed in the unit circle:
P^2 = |1 - z|^2
= (1 - cos(2pi/5))^2 + (sin(2pi/5))^2
= 2 - 2 cos(2pi/5)
= 2 - phi
Next let's compute D, the length of the side of a decagon inscribed
in the unit circle! We can mimic the last stage of the above
calculation, but with an angle half as big:
D^2 = 2 - 2 cos(pi/5)
To go further, we can use a half-angle formula:
cos(pi/5) = sqrt((1 + cos(2pi/5))/2)
= sqrt(1/2 + phi/4)
This gives
D^2 = 2 - sqrt(2 + phi)
But we can simplify this a bit more. As any lover of the golden ratio
should know,
2 + phi = 2.6180339...
is the square of
1 + phi = 1.6180339...
So we really have
D^2 = 1 - phi
Okay. Your eyes have glazed over by now - unless you've secretly been
waiting all along for This Week's Finds to cover high-school algebra
and trigonometry. But we're done. We see that
P^2 = H^2 + D^2
simply says
2 - phi = 1 + (1 - phi)
That wasn't so bad, but imagine discovering it and proving it using
axiomatic geometry back around 300 BC! How did they do it?
For this, let's turn to
20) Ian Mueller, Philosophy of Mathematics and Deductive Structure in
Euclid's Elements, MIT Press, Cambridge Massachusetts, 1981.
This is reputed to be be the most thorough investigation of the
logical structure of Euclid's Elements! And starting on page 257 he
discusses how people could have discovered this fact by staring at
an icosahedron!
This should not be too surprising. After all, there are pentagons,
hexagons and decagons visible in the icosahedron. But I was stuck
until I cheated and read Mueller's explanation.
If you hold an icosahedron so that one vertex is on top and one is
on bottom, you'll see that its vertices are arranged in 4 horizontal
layers. From top to bottom, these are:
1 vertex on top
5 vertices forming a pentagon: the "upper pentagon"
5 vertices forming a pentagon: the "lower pentagon"
1 vertex on bottom
Pick a vertex from the upper pentagon: call this A. Pick a vertex
as close as possible from the lower pentagon: call this B. A is not
directly above B. Drop a vertical line down from A until it hits the
horizontal plane on which B lies. Call the resulting point C.
If you think about this, or better yet draw it, you'll see that ABC
is a right triangle. And if we apply the Pythagorean theorem to
this triangle we'll get the equation
P^2 = H^2 + D^2
To see this, we only need to check that:
* the length AB equals the edge of a pentagon inscribed in a circle;
* the length AC equals the edge of a hexagon inscribed in a circle;
* the length BC equals the edge of a decagon inscribed in a circle.
Different circles, but of the same radius! What's this radius?
Take all 5 vertices of the "upper pentagon". These lie on a circle,
and this circle has the right radius.
Using this idea, it's easy to see that the length AB equals the edge
of a pentagon inscribed in a circle. It's also easy to see that
BC equals the edge of a decagon inscribed in a circle of the same
radius. The hard part, at least for me, is seeing that AC equals the
edge of a hexagon inscribed in a circle of the same radius... or in
other words, the radius of that circle! (The hexagon seems to be a
red herring.)
To prove this, we need a wonderful fact: the distance between the
"upper pentagon" and the "lower pentagon" equals the radius of
circle containing the vertices of the upper pentagon!
Can you prove this?
I just found a very beautiful proof. I could explain it easily with
lots of pictures, but I'm too lazy to draw them electronically. I
don't feel too guilty about this, though: I've given enough clues for
you to figure everything out and draw the pictures yourself. It's
lots of fun. And if you draw nice electronic pictures, I'd love to
include them here and credit you!
Okay, okay... I'll give you one more hint. Consider the "top" vertex
of the icosahedron and the 5 vertices forming the "upper pentagon".
Let a be any vertex on the upper pentagon, and let b be the top
vertex. Drop a vertical line from the top vertex until it hits the
plane of the upper pentagon; call the point where it hits c. Prove
that the points a, b, and c form a right triangle congruent to the
right triangle ABC. And using this, show the distance between the
"upper pentagon" and the "lower pentagon" equals the radius of the
circle containing the vertices of the upper pentagon!
So, we also get:
* the length ab equals the edge of a pentagon inscribed in a circle;
* the length ac equals the edge of a hexagon inscribed in a circle;
* the length bc equals the edge of a decagon inscribed in a circle.
I thank Toby Bartels for help with some of this stuff.
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Quote of the Week:
"Geometry enlightens the intellect and sets one's mind right. All
its proofs are very clear and orderly. It is hardly possible for
errors to enter into geometric reasoning, because it is well arranged
and orderly. Thus the mind that constantly applies itself to geometry
is unlikely to fall into error...." - Ibn Khaldun
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If you just want the latest issue, go to
Archimedes Plutonium
Why is UCR John Baez a failure in math and physics, cannot even take 9 times 105 and see that it is 945? I mean, well, why ever bother with the mindless Weinberg-Glashow-Gell-Mann Standard Model nonsense of physics, as some sort of Algebra, when you cannot do 9x105=945 and interpret it correctly of what you have done in physics.
Much the same problem with Marcela Carena of Fermi Natl. Lab with the excessive muon spin as reported in Scientific American, Oct2021. Not able to ask the most simple and basic question of physics, which is the atom's true real electron is it the muon stuck inside a 840MeV proton torus or is it the 0.5MeV particle that AP says is the Dirac magnetic monopole. No, Marcela Carena and John Baez rather listen to a herd community, rather than practice and do physics with a logical mind-- ask the simple questions and do the logical experiments from those logical questions.
Physics, left up to Baez and his buddies of Weinberg, Glashow, Gell-Mann, Peter Higgs, Ed Witten those buddies are comfortable with a electron at 0.5MeV, proton at 938MeV, neutron at 940MeV and all three of them as "do nothing particles" with the amazing audacity of saying the 0.5MeV particle flys around the outside of a 938MeV proton at nearly the speed of light 99.99% speed of light, yet never flys off. For Baez, and his buddies never understood Angular Momentum. Never could interpret 9 x 105 = 938 or 940 within Sigma Error.
But then along comes AP, and says-- sigma error is important in physics and use it.
AP says-- you cannot have "do nothing particles in physics".
AP says-- the true electron of atoms is the muon and stuck inside a 840MeV proton doing the Faraday law by producing Dirac magnetic monopoles such as the 0.5MeV dipole as electricity.
Is John Baez or Sheldon Glashow or Peter Higgs or Ed Witten still able to learn in science, or are they just complete washed up and washed out. Are they complete wash out failures of physics? Probably complete failures because they cannot even muster the intelligence of dropping a Kerr or Mason lid inside a folded up paper cone and acknowledge something as simple as what a High School student can prove, that a slant cut in cone is a Oval, never the ellipse, (see AP books below). Yet that is what the "pack of fools Baez, Glashow, Higgs, Witten" still teach their electron is 0.5MeV, their ellipse is slant cut in cone, but probably worst of all, these bozos still teach the Boole logic of 2 OR 1= 3 with AND as subtraction. Imagine that, physics professors who cannot even think logically correct, no wonder they are incapable of 9 x 105.
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3rd published book
AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.
Length: 21 pages
File Size: 1620 KB
Print Length: 21 pages
Publication Date: March 11, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PLSDQWC
Text-to-Speech: Enabled
X-Ray: Not Enabled
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled
#8-2, 11th published book
World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)
Last revision was 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?
Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.
Length: 137 pages
Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1307 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 137 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)
74th published book
HISTORY OF THE PROTON MASS and the 945 MeV //Atom Totality series, book 3 Kindle Edition
by Archimedes Plutonium (Author)
In 2016-2017, AP discovered that the real proton has a mass of 840 MeV, not 938. The real electron was actually the muon and the muon stays inside the proton that forms a proton torus of 8 rings and with the muon as bar magnet is a Faraday Law producing magnetic monopoles. So this book is all about why researchers of physics and engineers keep getting the number 938MeV when they should be getting the number 840 MeV + 105 MeV = 945 MeV.
Cover Picture is a proton torus of 8 rings with a muon of 1 ring inside the proton torus, doing the Faraday Law and producing magnetic monopoles.
Length: 17 pages
Product details
• Publication Date : December 18, 2019
• Word Wise : Enabled
• Print Length : 17 pages
• File Size : 698 KB
• ASIN : B082WYGVNG
• Language: : English
• Text-to-Speech : Not enabled
• Enhanced Typesetting : Enabled
• Screen Reader : Supported
• X-Ray : Not Enabled
• Lending : Enabled
#1-4, 105th published book
Atom Geometry is Torus Geometry // Atom Totality series, book 4 Kindle Edition
by Archimedes Plutonium (Author)
Since all atoms are doing the Faraday Law inside them, of their thrusting muon into a proton coil in the shape of a geometry torus, then the torus is the geometry of each and every atom. But then we must explain the neutrons since the muon and proton are doing Faraday's Law, then the neutron needs to be explained in terms of this proton torus with muon inside, all three shaped as rings. The muon is a single ring and each proton is 8 rings. The neutron is shaped like a plate and is solid not hollow. The explanation of a neutron is that of a capacitor storing what the proton-muon rings produce in electricity. Where would the neutron parallel plates be located? I argue in this text that the neutron plates when fully grown from 1 eV until 945MeV are like two parallel plate capacitors where each neutron is part of one plate, like two pieces of bread with the proton-muon torus being a hamburger patty.
Cover Picture: I assembled two atoms in this picture where the proton torus with a band of muons inside traveling around and around the proton torus producing electricity. And the pie-plates represent neutrons as parallel-plate capacitors.
Length: 39 pages
Product details
• Publication Date : March 24, 2020
• Word Wise : Not Enabled
• ASIN : B086BGSNXN
• Print Length : 39 pages
• File Size : 935 KB
• Language: : English
• Text-to-Speech : Not enabled
• Screen Reader : Supported
• X-Ray : Not Enabled
• Enhanced Typesetting : Enabled
• Lending : Enabled
Amazon Best Sellers Rank: #1,656,820 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#6413 in Mathematics (Kindle Store)
#315 in One-Hour Science & Math Short Reads
#4953 in Physics (Kindle Store)
#1-5, 112th published book
New Perspective on Psi^2 in the Schrodinger Equation in a Atom Totality Universe// Atom Totality series, book 5
Kindle Edition
by Archimedes Plutonium (Author)
I first heard of the Schrodinger equation in college chemistry class. We never actually did any problem solving with the equation, and we were only told about it. Then taking physics my next year in college and after I bought the Feynman Lectures on Physics, just for fun for side reading, three volume set did I learn what this Schrodinger equation and the Psi^2 wavefunction was about. I am not going to teach the mathematics of the Schrodinger equation and the math calculations of the Psi or Psi^2 in this book, but leave that up to the reader or student to do that from Feynman's Lectures on Physics. The purpose of this book is to give a new and different interpretation of what Psi^2 is, what Psi^2 means. Correct interpretation of physics experiments and observations turns out to be one of the most difficult tasks in all of physics.
Cover Picture: a photograph taken of me in 1993, after the discovery of Plutonium Atom Totality, and I was 43 years old then, on a wintery hill of New Hampshire. It is nice that Feynman wrote a physics textbook series, for I am very much benefitting from his wisdom. If he had not done that, getting organized in physics by writing textbooks, I would not be writing this book. And I would not have discovered the true meaning of the Fine Structure Constant, for it was Feynman who showed us that FSC is really 0.0854, not that of 0.0072. All because 0.0854 is Psi, and Psi^2 is 0.0072.
Length: 20 pages
Product details
• ASIN : B0875SVDC7
• Publication date : April 15, 2020
• Language: : English
• File size : 1134 KB
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Enabled
• Print length : 20 pages
• Lending : Enabled
• Best Sellers Rank: #240,066 in Kindle Store (See Top 100 in Kindle Store)
◦ #5 in 30-Minute Science & Math Short Reads
◦ #65 in General Chemistry & Reference
◦ #481 in Physics (Kindle Store)
#1-6, 135th published book
QED in Atom Totality theory where proton is a 8 ring torus and electron = muon inside proton doing Faraday Law// Atom Totality series, book 6 Kindle Edition
by Archimedes Plutonium (Author)
Since the real true electron of atoms is the muon and is a one ring bar magnet thrusting through the 8 ring torus of a proton, we need a whole entire new model of the hydrogen atom. Because the Bohr model with the 0.5MeV particle jumping orbitals as the explanation of Spectral Lines is all wrong. In this vacuum of explaining spectral line physics, comes the AP Model which simply states that the hydrogen atom creates Spectral lines because at any one instant of time 4 of the 8 proton rings is "in view" and the electricity coming from those 4 view rings creates spectral line physics.
Cover Picture: Is a imitation of the 8 ring proton torus, with my fingers holding on the proton ring that has the muon ring perpendicular and in the equatorial plane of the proton rings, thrusting through. This muon ring is the same size as the 8 proton rings making 9 x 105MeV = 945MeV of energy. The muon ring has to be perpendicular and lie on the equator of the proton torus. Surrounding the proton-torus would be neutrons as skin or coating cover and act as capacitors in storing the electricity produced by the proton+muon.
Product details
• ASIN : B08K47K5BB
• Publication date : September 25, 2020
• Language : English
• File size : 587 KB
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Not Enabled
• Print length : 25 pages
• Lending : Enabled
• Best Sellers Rank: #291,001 in Kindle Store (See Top 100 in Kindle Store)
◦ #13 in 45-Minute Science & Math Short Reads
◦ #52 in General Chemistry & Reference
◦ #334 in General Chemistry
#1-7, 138th published book
The true NUCLEUS of Atoms are inner toruses moving around in circles of a larger outer torus// Rutherford, Geiger, Marsden Experiment revisited // Atom Totality Series, book 7 Kindle Edition
by Archimedes Plutonium (Author)
The geometry of Atoms of the Table of Chemical Elements is torus geometry. We know this to be true for the torus geometry forms the maximum electricity production when using the Faraday Law. We see this in Old Physics with their tokamak toruses attempting to make fusion, by accelerating particles of the highest possible acceleration for the torus is that geometry. But the torus is the geometry not only of maximum acceleration but of maximum electrical generation by having a speeding bar magnet go around and around inside a torus== the Faraday law, where the torus rings are the copper closed wire loop. The protons of atoms are 8 loops of rings in a torus geometry, and the electron of atoms is the muon as bar magnet, almost the same size as the proton loops but small enough to fit inside proton loops. It is torus geometry that we investigate the geometry of all atoms.
Length: 41 pages
Product details
• Publication Date : October 9, 2020
• File Size : 828 KB
• Word Wise : Not Enabled
• Print Length : 41 pages
• ASIN : B08KZT5TCD
• Language: : English
• Text-to-Speech : Not enabled
• Enhanced Typesetting : Enabled
• Screen Reader : Supported
• X-Ray : Not Enabled
• Lending : Enabled
#1-8, 1st published book
Atom Totality Universe, 8th edition, 2017// A history log book: Atom Totality Series book 8 Kindle Edition
by Archimedes Plutonium (Author)
Last revision 7Apr2021. This was AP's first published science book.
Advisory: This is a difficult book to read and is AP's research log book of the Atom Totality in 2016-2017. I want to keep it for its history value. AP advises all readers wanting to know the Plutonium Atom Totality theory to go to the 9th edition that is the latest up to date account of this theory. The reason AP wants to keep the 8th edition is because of Historical Value, for in this book, while writing it, caused the discovery of the real electron is the muon of atoms. The real proton of atoms is 840MeV and not the 938MeV that most books claim. The particle discovered by JJ Thomson in 1897 thinking he discovered the electron of atoms was actually the Dirac magnetic monopole at 0.5MeV. This discovery changes every, every science that uses atoms and electricity and magnetism, in other words, every science.
Foreward:
I wrote the 8th edition of Atom Totality and near the end of writing it in 2017, I had my second greatest physics discovery. I learned the real electron of atoms was the muon at 105MeV and not the tiny 0.5MeV particle that J.J.Thomson found in 1897. So I desperately tried to include that discovery in my 8th edition and it is quite plain to see for I tried to write paragraphs after each chapter saying as much. I knew in 2017, that it was a great discovery, changing all the hard sciences, and reframing and restructuring all the hard sciences.
Length: 632 pages
Product details
File Size: 1132 KB
Print Length: 632 pages
Publication Date: March 11, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PLP9NDR
Text-to-Speech: Enabled
X-Ray: Not Enabled
Word Wise: Enabled
Lending: Enabled
Screen Reader: Supported
Enhanced Typesetting: Enabled
Amazon Best Sellers Rank: #578,229 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#1610 in Physics (Kindle Store)
#8526 in Physics (Books)
#18851 in Biological Sciences (Books)
#2-1, 137th published book
Introduction to AP's TEACHING TRUE PHYSICS// Physics textbook series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
#1 New Release in Electromagnetic Theory
This will be AP's 137th published book on science. And the number 137 is special to me for it is the number of QED, Quantum Electrodynamics as the inverse fine structure constant. I can always remember 137 as that special constant of physics and so I can remember where Teaching True Physics was started by me.
Time has come for the world to have the authoritative textbooks for all of High School and College education. Written by the leading physics expert of the time. The last such was Feynman in the 1960s with Feynman Lectures on Physics. The time before was Maxwell in 1860s with his books and Encyclopedia Britannica editorship. The time is ripe in 2020 for the new authoritative texts on physics. It will be started in 2020 which is 60 years after Feynman. In the future, I request the physics community updates the premier physics textbook series at least every 30 years. For we can see that pattern of 30 years approximately from Faraday in 1830 to Maxwell in 1860 to Planck and Rutherford in about 1900, to Dirac in 1930 to Feynman in 1960 and finally to AP in 1990 and 2020. So much happens in physics after 30 years, that we need the revisions to take place in a timely manner. But also, as we move to Internet publishing such as Amazon's Kindle, we can see that updates can take place very fast, as editing can be a ongoing monthly or yearly activity. I for one keep constantly updating all my published books, at least I try to.
Feynman was the best to make the last authoritative textbook series for his concentration was QED, Quantum Electrodynamics, the pinnacle peak of physics during the 20th century. Of course the Atom Totality theory took over after 1990 and all of physics; for all sciences are under the Atom Totality theory.
And as QED was the pinnacle peak before 1990, the new pinnacle peak is the Atom Totality theory. The Atom Totality theory is the advancement of QED, for the Atom Totality theory primal axiom says -- All is Atom, and atoms are nothing but Electricity and Magnetism.
Length: 64 pages
Product details
• File Size : 790 KB
• Publication Date : October 5, 2020
• Word Wise : Enabled
• Print Length : 64 pages
• Text-to-Speech : Not enabled
• Screen Reader : Supported
• Enhanced Typesetting : Enabled
• X-Ray : Not Enabled
• Language: : English
• ASIN : B08KS4YGWY
• Lending : Enabled
• Best Sellers Rank: #430,602 in Kindle Store (See Top 100 in Kindle Store)
◦ #39 in Electromagnetic Theory
◦ #73 in Electromagnetism (Kindle Store)
◦ #74 in 90-Minute Science & Math Short Reads
#2-2, 145th published book
TEACHING TRUE PHYSICS//Junior High School// Physics textbook series, book 2
Kindle Edition
by Archimedes Plutonium (Author)
What I am doing is clearing the field of physics, clearing it of all the silly mistakes and errors and beliefs that clutter up physics. Clearing it of its fraud and fakeries and con-artistry. I thought of doing these textbooks starting with Senior year High School, wherein I myself started learning physics. But because of so much fraud and fakery in physics education, I believe we have to drop down to Junior year High School to make a drastic and dramatic emphasis on fakery and con-artistry that so much pervades science and physics in particular. So that we have two years in High School to learn physics. And discard the nonsense of physics brainwash that Old Physics filled the halls and corridors of education.
Product details
• ASIN : B08PC99JJB
• Publication date : November 29, 2020
• Language: : English
• File size : 682 KB
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Enabled
• Print length : 78 pages
• Lending : Enabled
• Best Sellers Rank: #185,995 in Kindle Store (See Top 100 in Kindle Store)
◦ #42 in Two-Hour Science & Math Short Reads
◦ #344 in Physics (Kindle Store)
◦ #2,160 in Physics (Books)
#2-3, 146th published book
TEACHING TRUE PHYSICS// Senior High School// Physics textbook series, book 3
Kindle Edition
by Archimedes Plutonium (Author)
I believe that in knowing the history of a science is knowing half of that science. And that if you are amiss of knowing the history behind a science, you have only a partial understanding of the concepts and ideas behind the science. I further believe it is easier to teach a science by teaching its history than any other means of teaching. So for senior year High School, I believe physics history is the best way of teaching physics. And in later years of physics courses, we can always pick up on details. So I devote this senior year High School physics to a history of physics, but only true physics. And there are few books written on the history of physics, so I chose Asimov's The History of Physics, 1966 as the template book for this textbook. Now Asimov's book is full of error and mistakes, and that is disappointing but all of Old Physics is full of error. On errors and mistakes of Old Physics, the best I can do is warn the students, and the largest warning of all is that whenever someone in Old Physics says "electron" what they are talking about is really the Dirac magnetic monopole. And whenever they talk about the Rutherford-Bohr model of the atom, they are talking about huge huge grave mistakes, for the true atom is protons as 8 ringed toruses with a muon stuck inside of a proton doing the Faraday law and producing those magnetic monopoles as electricity. I use Asimov's book as a template but in the future, I hope to rewrite this textbook using no template at all, that is if I have time in the future.
Cover Picture: Is the book The History of Physics, by Isaac Asimov, 1966 and on top of the book are 4 cut-outs of bent circles representing magnetic monopoles which revolutionizes modern physics, especially the ElectroMagnetic theory.
Product details
• ASIN : B08RK33T8V
• Publication date : December 28, 2020
• Language : English
• File size : 794 KB
• Text-to-Speech : Enabled
• Screen Reader : Supported
• Enhanced typesetting : Enabled
• X-Ray : Not Enabled
• Word Wise : Enabled
• Print length : 123 pages
• Lending : Enabled
• Best Sellers Rank: #4,167,235 in Kindle Store (See Top 100 in Kindle Store)
◦ #15,099 in Physics (Kindle Store)
◦ #91,163 in Physics (Books)
#3-1, 2nd published book
True Chemistry: Chemistry Series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
Physics and chemistry made a mistake in 1897 for they thought that J.J. Thomson's small particle of 0.5MeV was the electron of atoms. By 2017, Archimedes Plutonium discovered that the rest mass of 940 for neutron and proton was really 9 x 105MeV with a small sigma-error. Meaning that the real proton is 840MeV, real electron is 105 MeV= muon, and that little particle Thomson discovered was in fact the Dirac magnetic monopole. Dirac circa 1930s was looking for a magnetic monopole, and sadly, Dirac passed away before 2017, because if he had lived to 2017, he would have seen his long sought for magnetic monopole which is everywhere.
Cover picture: shows 3 isomers of CO2 and the O2 molecule.
Length: 1150 pages
Product details
• File Size : 2167 KB
• ASIN : B07PLVMMSZ
• Publication Date : March 11, 2019
• Word Wise : Enabled
• Print Length : 1150 pages
• Language: : English
• Text-to-Speech : Not enabled
• Enhanced Typesetting : Enabled
• X-Ray : Not Enabled
• Lending : Enabled
Amazon Best Sellers Rank: #590,212 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#181 in General Chemistry & Reference
#1324 in General Chemistry
#1656 in Physics (Kindle Store)
3rd published book
AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.
Length: 21 pages
File Size: 1620 KB
Print Length: 21 pages
Publication Date: March 11, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PLSDQWC
Text-to-Speech: Enabled
X-Ray: Not Enabled
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled
11th published book
World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)
Last revision was 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?
Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.
Length: 137 pages
Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1307 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 137 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)
5th published book
Suspend all College Classes in Logic, until they Fix their Errors // Teaching True Logic series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
Last revision was 29Mar2021. This is AP's 5th published book of science.
Preface:
First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.
The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = either 3 or 2 but never 5, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). The AND connector in Logic stems from the idea, the mechanism involved, that given a series of statements, if just one of those many statements has a true truth value, then the entire string of statements is overall true, and thus AND truth table is truly TTTF and never TFFF. And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.
My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.
Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.
Length: 72 pages
File Size: 773 KB
Print Length: 72 pages
Publication Date: March 12, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PMB69F5
Text-to-Speech: Enabled
X-Ray: Not Enabled
Word Wise: Not Enabled
Lending: Enabled
Screen Reader: Supported
Enhanced Typesetting: Enabled
y z
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|/______ x
More people reading and viewing AP's newsgroup than viewing sci.math, sci.physics. So AP has decided to put all NEW WORK, to his newsgroup. And there is little wonder because in AP's newsgroups, there is only solid pure science going on, not a gang of hate spewing misfits blighting the skies.
In sci.math, sci.physics there is only stalking hate spew along with Police Drag Net Spam of no value and other than hate spew there is Police drag net spam day and night.
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of stalkers and spammers, Police Drag Net Spam that floods each and every day, book and solution manual spammers, off-topic-misfits, front-page-hogs, churning imbeciles, stalking mockers, suppression-bullies, and demonizers. And the taxpayer funded hate spew stalkers who ad hominem you day and night on every one of your posts.
There is no discussion of science in sci.math or sci.physics, just one long line of hate spewing stalkers followed up with Police Drag Net Spam (easy to spot-- very offtopic-- with hate charged content). And countries using sci.physics & sci.math as propaganda platforms, such as tampering in elections with their mind-rot.
Read my recent posts in peace and quiet.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium