1.
Sphere Packing in Curved 3D Space
The densest possible packing of four spheres in flat 3D space is given by the tetrahedral arrangement, but this arrangement can't be used to fill space ...
2.
Doppler Shift for Sound and Light
In contrast, the relativistic Doppler shift for light, with cs = c, does not distinguish between emitter and absorber motion, but simply predicts a ...
3.
Numbers Expressible As (a^2 - 1)(b^2 - 1)
Some time ago I mentioned that the number 588107520 is expressible in the form (X^2 - 1)(Y^2 - 1) (where X,Y are integers) in five distinct ways, ...
4.
Reducing Quartics to Cubics
Thus, it can be added to the well known methods of Ferrari and Descartes for reducing quartics to cubics. Given any quartic Ax^4 + Bx^3 + Cx^2 + Dx + E = 0 ...
5.
Archimedes and the Square Root of 3
How he managed to extract his square roots with such accuracy...is one of the puzzles that this extraordinary man has bequeathed to us. ...
6.
The Sagnac Effect
These effects have been confirmed empirically by, for example, the Michelson-Morley experiment. Considering the Earth as a particle on a large Sagnac device ...
7.
Old Notes on Curvature
Old Notes on Curvature. The extrinsic curvature of a surface embedded in a higher .... is the mean value of the curvature over all possible directions. ...
8.
Franklin's Magic Squares
Franklin then described an 8x8 magic square he had devised in his youth, .... even in the size of my square, I went home and made that evening the following ...
9.
Solving Magic Squares
It turns out that the sum of cubes just gives equation (1) again, ... Thus, with 4x4 magic squares, instead of working with the values 1 through 16 we ... 11 -1 7 15 -7 -15 -5 15 5 -15 For both of these squares we have g=-9, h=3, k=11, ...
10.
MathPages: History
History. Mercurius in Sole Visus · The Thought of a Thought - Edgar Allan Poe · The Prismoidal Formula · Gerber's Gravity · Harmonia Mensurarum ...
