Beauty in Mathematics

primi sui motori con e-max

   Beauty in Mathematics

La rivista The Mathematical Intelligencer nel n. 4/1988 propose ai suoi lettori la seguente lista di 24 risultati al fine di effettuare una indagine sulle formule ritenute più belle.

 

A

Euler's formula for a polyhedron: V + F =E + 2. M At any party, there is a pair of people who
have the same number of friends present.

B

Any square matrix satisfies its characteristic equation

N

The number of partitions of an integer into
odd integers is equal to the number of partitions into distinct integers.

C

5{(1 – x5)(1 – x10)(1 – X15) . . . }
{(1 – x)(1 – x2)(1 – x3 )(1 – x4). . . }6
          = p(4) + p(9)xp(14)x2 +. . .
where p(n) is the number of partitions of n.

O

If the points of the plane are each coloured
red, yellow, or blue, there is a pair of
points of the same colour of mutual distance unity.

D

The number of primes is infinite.

P

Every plane map can be coloured with 4
colours.

E

There is no rational number whose square is 2

Q

A continuous mapping of the closed unit
disk into itself has a fixed point.

F

Every prime of the form 4n + 1 is the sum
of two integral squares in exactly one way.

R

Write down the multiples of root 2, ignoring fractional parts, and underneath the numbers missing from the first sequence.
   1    2    4    5     7     8     9      11     12 ...
   3    6   10  13  17   20    23     27     30 …
The difference is 2n in the nth place.

G

1 + 1/22 + 1/31/41/5+ … =  p 2/6.

S

A regular icosahedron inscribed in a regular octagon divides the edges in the Colden Ratio.

H

      1         -         1        +         1       
2 x 3 x 4        4 x 5 x 6         6 x 7 x 8

- ….. = p - 3 . 
               4

T

The number of representations of an odd number as the sum of 4 squares is 8 times the sum of its divisors; of an even number, 24 times the sum of its odd divisors.

I

p  is transcendental.

U

The word problem for groups is unsolvable.

J

Every number greater than 77 is the sum of
integers, the sum of whose reciprocals is l.

V

The order of a subgroup divides the order of the group.

K

The maximum area of a quadrilateral withsides a, b, c, d is {(s-a)(s-b)(s-c)(s-d)}½,where s is half the perimeter.

W

eip - 1.

L

There is no equilateral triangle whose vertices are plane lattice points.

X

There are 5 regular polyhedra.
primi sui motori con e-max