Batman Equation

[Rex Boggs]

Check out
http://www.gizmodo.com.au/2011/07/the-batman-equation/
and
http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real

Anyone care to put the equations into a tinspire? Might be a good job for a keen student.

Lots of maths in this.

Cheers

Rex

[Nelson Sousa]

That's an implicit equation, that the Nspire does not support.

It needs to ben either solved for y (which doesn't seem easy if at all possible) or parametrized which can also be quite hard.

The Voyage 200 and TI-89 do implicit equations but this one may be painfully slow to plot.

--
Nelson Sousa

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[Jim Fullerenex]

Are you sure, Nelson? :)

To tell the truth, I find myself quite crazy on even attempting to start. And I have always kept in mind (from my previous experiences) that Nspire is very unhappy with abs(). The absolute values always stir things up, introducing the notorious sign() in possibly a total mess, which I personally dislike a lot.

Warning: never ever copy that hell long batman equation into the graphing page directly!!! 

Observing that the equation actually consists of six parts multiplied to zero, I try to draw the parts separately.

Attached screenshot:

1. defining individual terms

2. graph, do some modification, reset color and done!

Best,

Jim

2011/11/4 Nelson Sousa <nso...@gmail.com>

[Jim Fullerenex]

Hi,

Half an hour. I packed the messy functions and expressions into a document with detailed explanation. (and a better batman logo :) )

Hope you like it!!!

Best,

Jim

2011/11/4 Jim Fullerenex <smoa...@gmail.com>

[Jim Fullerenex]

Add: screen shots for those who'd like a quick view.

Also I want to thank Rex for this great (and interesting) idea.

Cheers,

[Nelson Sousa]

nicely done!!

[Jim Fullerenex]

Yeah... :D  sometimes Nspire can be more powerful than the manual claims.

Cheers,

[Rex Boggs]

Great work, Jim!

 

If folks want to find out how these equations actually generate the graphs, go to

http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real

and scroll down.   One chap explains which “factors” (actually equations) are responsible for each section of the graph.

 

There is a lot of good math in all of this, worth exploring.

 

Cheers

 

Rex

Jim

2011/11/4 Jim Fullerenex <smoa...@gmail.com>

Best,

Jim

2011/11/4 Jim Fullerenex <smoa...@gmail.com>

Best,

Jim

2011/11/4 Nelson Sousa <nso...@gmail.com>

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To post to this group, send email to tins...@googlegroups.com

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For more options, visit this group at
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The tns documents shared by group members are archived at
https://sites.google.com/site/tinspiregroup/classroom-news/welcome-abouttime

[Jim Fullerenex]

Yep... The six parts are split and shown separately in "Batman equation.tns" Page 1.4 (though the final effect is a complete logo). Those who want to explore how different parts work can simply press "tab" and view function f1 to f6.

Best,

Jim

2011/11/4 Rex Boggs <rexb...@optusnet.com.au>

[Jim Fullerenex]

One more implicit graph: the Love equation. 

Just to give another cool example.

Btw, Nelson, I never know TI-89 can do implicit graphing. My friend shows me the graph-type menu on TI-89 titanium, which seems to include only the following: "1. Function; 2. Parametric; 3. Polar; 4. Sequence; 5. 3D; 6. Diff Equations" 

All of these are included in Nspire OS 3.x. Have I missed anything?

[John Hanna]

When you choose 3D on the TI-89 you can change the type from surface to contour to implicit, but I forget how!

 

     John Hanna

     jeh...@optonline.net

     www.johnhanna.us

     T³ - Teachers Teaching with Technology

     "A cowchip is paradise to a fly."

 

---

[Travis Bower]

CAS only, right?

[Sean Bird]

zeros(expression, var) or specifically
zeros((x^2+y^2-1)^3-x^2*y^3,y)  is a CAS function.

3D works exactly the same on any TI-Nspire.
Similar to the zeros command, you can graph in 3D with zmin=0 and you can what the graph looks like
So you could graph z1(x,y)=(x^2+y^2-1)^3-x^2*y^3
and with
xmin=-2, xmax=2
ymin=-2, ymax=2
zmin= 0, zmax=1
Then press z to view it from the x-y plane.

The other graph that Jim showed would be z2(x,y)=x^(2)+(y-root(x^(2),3))^(2)-1
Increase the ymax to about 3.

[Travis Bower]

Thanks.

"Trying to find the z?" scroll down of course [it took me sec (=minutes) to figure it out; I'll save you the trouble.

--

[Sean Bird]

I had meant to attach 'this' version of Batman equation tns. It has a portion that will work on the numeric TI-Nspire.

There are a couple of videos showing how to do this which perhaps can save on any frustration of not finding the z range.
http://www.youtube.com/watch?v=MUdn46lvTuY

Part2 is found at
http://www.youtube.com/watch?v=qgIv-hjIXDc

Enjoy,
Sean Bird
Indianapolis, IN

[Jim Fullerenex]

Hi Sean,

Your 3D-2D implicit grapher is even cooler!!! That's indeed a very clever way. Thanks for the idea.

Btw, the 3D batman equation looks awful; I see that term3 and term5 are not working at all; term4 gives only 4 dots. I've tried to change document settings but the problem persists. Anyone has a tip of thought? I guess the culprit is still the messy nest of absolute values.

Best,

Jim

2011/11/6 Sean Bird <covena...@gmail.com>

[Nelson Sousa]

It's under Diamond+F on the 89 anv Voyage 200 if memory serves me
correctly. There you choose between wireframe, hidden surface,
implicit and contour.

Cheers,
Nelson