# 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