Scipsy

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of a particular color (commonly black and red, or sometimes yellow and red), and the object is to be the first to obtain four pieces in a horizontal, vertical, or diagonal line. Because the board is vertical, pieces inserted in a given column always drop to the lowest unoccupied row of that column. As soon as a column contains 6 pieces, it is full and no other piece can be placed in the column. Both players begin with 21 identical pieces, and the first player to achieve a line of four connected pieces wins the game. If all 42 men are played and no player has places four pieces in a row, the game is drawn. The game has been completely analyzed, so it is known that if both players play with optimal strategies, the first player can always win (Allis 1988). The numbers of possible positions after , 1, 2, … have been played is 1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, … . (via Connect-Four — from Wolfram MathWorld)

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of a particular color (commonly black and red, or sometimes yellow and red), and the object is to be the first to obtain four pieces in a horizontal, vertical, or diagonal line. Because the board is vertical, pieces inserted in a given column always drop to the lowest unoccupied row of that column. As soon as a column contains 6 pieces, it is full and no other piece can be placed in the column. Both players begin with 21 identical pieces, and the first player to achieve a line of four connected pieces wins the game. If all 42 men are played and no player has places four pieces in a row, the game is drawn. The game has been completely analyzed, so it is known that if both players play with optimal strategies, the first player can always win (Allis 1988). The numbers of possible positions after , 1, 2, … have been played is 1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, … . (via Connect-Four — from Wolfram MathWorld)

A vortex street on the circle is unstable (an old result of Thomson). Here we see 31 vortices inicially alligned on the circle. Integrated with Runge-Kutta with a Mathematica code allowing to evolve an arbitrary number of vortices. (via abel.math.harvard.edu)

A vortex street on the circle is unstable (an old result of Thomson). Here we see 31 vortices inicially alligned on the circle. Integrated with Runge-Kutta with a Mathematica code allowing to evolve an arbitrary number of vortices. (via abel.math.harvard.edu)

Antitoroid - Toroid Family 4 of 4

11111111,1=123456789876543,21


It *could* just be coincidence 
[…] a decent knowledge of mathematics reveals that correlation is not causation, that most coincidences actually are the result of chance

It *could* just be coincidence 

[…] a decent knowledge of mathematics reveals that correlation is not causation, that most coincidences actually are the result of chance

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Sketching Angles (by Kyle McDonald)
Handwritten corrections (by Open Library)