Description:
Mathematical discussions and pursuits.
|
|
|
Packing unit spheres in cubes: new results
|
| |
Eckard Specht has recently added to Packomania <[link]>
a new section about packing equal spheres in cubes.
And I have now found four improvements:
N = 47, 55, 56 and 57 unit spheres can be packed in cubes of side lengths
7.1449569471850588446953873413 2,
7.6374176888708342443174195154 3,... more »
|
|
Least Prime Factor function , lpf(i)
|
| |
If we divide that values of lpf(i) in three blocks such that:
A = values < p
B = values of p
C = values > p
then it happens that B/C = 1/(p-1) for certain intervals.
Further if x are the values of the argument of lpf(i) that satisfied
this condition then this values are periodic.
Example... more »
|
|
Rare Event...The Full Moon Strikes Again!
|
| |
...
I had in mind the famous conversation between Ramanujan and Hardy, in
which Hardy happened to mention the number 1729 and Ramanujan
instantly noted that it was the sum of cubes in two different ways.
That fact was obvious to Hardy as well, once alerted to it, for when
Hardy ("naturally") asked for a corresponding number for 4th powers... more »
|
|
|