OneWeirdDude/Nana shogi

OneWeirdDude/Pahoran

(In no particular order:)

• Total Eclipse of the Heart, by Bonnie Tyler
• Cat's in the Cradle, by Harry Chapin
• We Didn't Start the Fire, by Billy Joel
• Secret Agent Man, by Johnny Rivers
• Born to be Wild, Steppenwolf
• Axel F, by Harold Faltermeyer
• Within Attraction, Yanni
• Stayin' Alive, BeeGees
• Oh Yeah, by Yello
• Hotel California, The Eagles
• Lemmings DDR Remix
• What is Love, by Haddaway
• Chariots of Fire, by Vangelis
• Adiemus, by Karl Jenkins (not Enya)
• California Dreamin', by The Mamas and the Papas
• Wild Child, Enya
• That "soap opera lullaby", or whatever—with no words.
• In the Hall of the Mountain King, by Edvard Grieg
• Separate Ways, by Journey
• What's Up?, by 4 Non Blondes

(A little hobby of mine.)

i - The imaginary unit. Also the first index/counter, and the first quaternionic unit.

j - The imaginary unit in engineering. Also the second index/counter, and the second quaternionic unit.

k - The third index/counter, and the third quaternionic unit.

m - Integer to accompany n, when necessary.

n - General integer

r - The distance from the origin in polar coordinates, the distance from the z-axis in cylindrical coordinates, and in general the unsigned distance from (x, y) = (0, 0) in other coordinate systems.

u - x-component of w, in the complex numbers; also a common substitution in calculus, and a substitute integrand in integration by parts

v - y-component of w, in the complex numbers; also a substitute integrand in integration by parts

w - The fourth dimension, and the dependent variable in coordinate hyperspace.

• (Beyond four dimensions, x with subscripts are usually used; e.g. x₇ for the seventh dimension.)

Also the dependent variable in complex numbers, with components u, v.

x - The first variable usually learned in algebra class. Also the independent variable in spatial one-dimensional functions, and one of two or more such variables in two or more dimensions. Also the signed distance from the origin on the number line, or from the y-axis on the co-ordinate plane (abscissa), or from the yz-plane in co-ordinate space, or from the yzw-realm in co-ordinate hyperspace, etc.

y - The second such variable usually learned, and the dependent variable in spatial one-dimensional functions, and one of two or more independent variables in two or more dimensions. Also the signed distance from the x-axis on the co-ordinate plane (ordinate), or from the xz-plane in co-ordinate space, or from the xzw-realm in co-ordinate hyperspace, etc.

z - The third such variable usually learned, and the dependent variable in two-dimensional functions. Also the signed distance from the xy-plane, etc. Also the independent variable in C, the complex numbers, with components x, y.

• Collatz conjecture
• Fermat's Last Theorem
  • proved in 1994 by Andrew Wiles
• Four color theorem
  • proved by computer in 1976 by Kenneth Appel and Wolfgang Haken
  • improved in 1997 by Robertson, Sanders, Seymour, and Thomas
  • further improved and simplified in 2005, by Georges Gonthier
• Goldbach's conjecture
• formulas for roots of polynomials
  • cubic
    • depressed form solved by Scipione del Ferro (1465-1526), and later published in 1545 by Gerolamo Cardano (1502-1576)
    • general form solved by Cardano
    • special cases solved by Rafael Bombelli (ca. 1526-1573) in 1572
  • quartic: solved by Ludovico Ferrari (1522-1565)
  • quintic and higher degrees: proven to be impossible in 1824 by Niels Abel (1802-1829)
• odd perfect numbers
• classification of manifolds
  • ongoing for three dimensions
  • proved impossible in 4D by Andrey Markov Jr. in 1960
• tessellations of convex polygons
  • hexagons solved by Karl Reinhardt (three cases)
  • pentagons (ongoing):
    • five types discovered by Reinhardt
    • three more by Richard Brandon Kershner
    • a ninth by Richard E. James III
    • four more by Marjorie Rice (totaling 13)
    • a 14th by Rolf Stein
    • a 15th by Casey Mann, Jennifer McLoud-Mann, and David Von Derau