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) . . . }5
{(1 – x)(1 – x2)(1 – x3 )(1 – x4). . . }6
= p(4) + p(9)x+ p(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 + 1/32 + 1/42 + 1/52 + … = p 2/6. S
A regular icosahedron inscribed in a regular octagon divides the edges in the Golden Ratio. H
1 – 1 + 1
2 x 3 x 4 4 x 5 x 6 6 x 7 x 8– ….. = p – 3 .
4T
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.
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