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Did you know that..., part 3.
Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex.
You can position 10 defenders of a square castle so that on every side there will be 5 men.
There are many things that can be
multiplied
:
numbers
,
vectors
,
matrices
,
functions
,
equations
,
sets
, pegs...
A torus may be brushed smooth but a sphere can not.
A circle may be quite useful in drawing straight lines
.
In the sequence of all integers, there are arbitrary long runs with no primes.
With just one caveat, anything you can do with a compass and a ruler you can do with the ruler alone.
There are really
impossible things
.
You can
add apples and oranges
.
Complex number to a complex power may be real
.
Irrational number to an irrational power may be rational
.
There are trisectable angles that are not constructible
.
There exist triangular numbers that are also square
.
No two integers are equidistant from the square root of 2
Almost every integer has a digit 3 in it
C
0
- C
0
= [-1, 1]
The length of the diagonal of the unit square equals the square root of 2
Every composite number is the product of some factors and also the some of the same numbers
Simple quadrilaterals tessellate the plane
There is a simple solution to the affirmative action problem
Two simple polygons of equal area can be dissected into a finite number of congruent polygons
cos(36°) = (1 + √
5
)/4
1/3 + 1/4 = 7/12
Σ2
-n
= Σn·2
-n
Copyright © 1996-2008
Alexander Bogomolny
28699818
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