Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

Unique Properties of 7

• 7 is the smallest number that cannot be represented as a sum of 3 squares
• 7 is the smallest integer that is not the difference of two primes
• There are 7 frieze groups, infinite discrete symmetry groups for patterns on a strip (infinitely wide rectangle)
• The numbers on opposite sides of a regular die always add up to 7
• 7 is the minimum number of colors that is always sufficient to color any map on a torus
• 7 is the only prime followed by a cube
• 7 is the smallest n for which a regular polygon with n sides cannot be constructed with ruler and compass
• The Fano plane is the projective plane with the least number of points and lines: 7 each (submitted by Qiaochu Yuan)
• 7 is the smallest number of sides for a regular polygon to have non-integral angle measures in degrees
• 7 is the only dimension, besides the familiar 3, in which a vector cross product can be defined
• the periodic part of 1/7 is the smallest cyclic number. Moreover, it is the only cyclic number in decimal
• The Seven-Bridges-of-Königsberg problem started graph theory
• one needs at least 7 riffle shuffles to randomize a deck of cards
• a seven-segment display is used on electronic devices and can display any digit
• any obtuse triangle can be dissected into 7 acute triangles, and 7 is the smallest such number
• 7 is the largest prime that is a sum of the first several consecutive Fibonacci numbers
• 7 is the smallest prime that is not one more than a power of two