 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
The Ramanujan Pages |
|
|
|
by Titus Piezas III |
|
|
|
(NEW!) If you like mathematical identities, check out "A Collection of Algebraic Identities" by this author. |
|
|
|
See also: http://mathworld.wolfram.com/topics/Piezas.html |
|
|
|
Hello and welcome to our little fox hole.
Here you will find articles written by my owner on topics that Ramanujan worked on, topics my owner found really fascinating and which he hopes you would, too.
So read a sample and enjoy! For number theory, please jump to Page 9. |
|
|
|
 |
|
|
|
|
|
 |
|
|
|
|
|
I. Ramanujan's Constant (e^(Pi*sqrt(163))) and Its Cousins |
|
|
|
II. On Keen Approximations |
|
|
|
III. Pi Formulas, Ramanujan, and the Baby Monster Group |
|
|
|
IV. On Ramanujan's Other Pi Formulas |
|
|
|
V. The k-function: Extending Ramanujan's Dedekind Eta Quotients (Part 1) |
|
|
|
VI. The k-function: Continued Fractions and Platonic Solids (Part 2) |
|
|
|
VII. Ramanujan's Cubic Continued Fraction (And Others) |
|
|
|
|
|
VIII. The Degen-Graves-Cayley Eight-Square Identity |
|
|
|
IX. Ramanujan and The Cubic Equation 3^3+4^3+5^3 = 6^3 |
|
|
|
IXb. The Equation q1^3+q2^3+q3^3+q4^3 = (a^3+b^3+c^3+d^3)q5^3 |
|
|
|
X. Ramanujan and The Quartic Equation 2^4+2^4+3^4+4^4+4^4 = 5^4 |
|
|
|
XI. Euler's Extended Conjecture and a^k+b^k+c^k = d^k for k > 4 |
|
|
|
XII. Timeline of Euler's Extended Conjecture |
|
|
|
XIII. Taxicab Numbers & Fermat Surface a^k+b^k = c^k+d^k for k = 4, 6, 8 |
|
|
|
XIV. Ramanujan and Fifth Power Identities |
|
|
|
XV. Binary Quadratic Forms as Equal Sums of Like Powers |
|
|
|
XVI. Binary Quadratic Forms as Arnold's Perfect Forms |
|
|
|
XVII. Curious Properties of j-Function Formulas |
|
|
|
If you also like solvable equations (cubics, quartics, quintics, etc.) may I suggest the
Homepage |
|
|
|
About the author:
An early thirty-something who teaches philosophy in university. Also interested in the sciences and mathematics, especially number theory. (Though for the ancient Greeks all these fields of knowledge were one and the same.)
Likes to travel. Been to Canada, France, Australia, South Africa, China, HongKong, Singapore, Indonesia, Philippines.
Also likes to read books and watch movies. (They are, after all, just other ways to travel.)
tpiezasIII@gmail.com -> (remove "III" for email) |
|
|
|
This webpage was born Mar. 31, 2005. |
|
|
|
|
|
