Math Newsletter number 22; Wednesday, December 22, 2010.

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http://www2.stetson.edu/~efriedma/numbers.html

What's Special About This Number?

If you know a distinctive fact about a number not listed

here, please e-mail me.

efriedma@stetson.edu

http://www.goiit.com/posts/list/0/community-shelf-every-

number-is-special-78754.htm

http://www.numbergossip.com

0 is the additive identity.

http://en.wikipedia.org/wiki/Additive_identity

1 is the multiplicative identity.

http://en.wikipedia.org/wiki/Identity_element

1 is the only positive integer that is neither prime nor

composite

http://www.numbergossip.com/1

2 is the only even prime.

http://www.blurtit.com/q228557.html

2 is the smallest positive prime number.

http://www.numbergossip.com/2

For any polyhedron, 2 is the number of vertices plus the

number of faces minus the number of edges.

http://www.mathsisfun.com/geometry/vertices-faces-edges.html

3 is the number of spatial dimensions we live in.

http://en.wikipedia.org/wiki/Dimension

http://news.softpedia.com/news/What-Are-the-Spatial-

Dimensions-16390.shtml

3 is the greatest number of consecutive integers that can be

pairwise relatively prime.

http://primes.utm.edu/glossary/xpage/PairwiseRelativelyPrime.

html

3 is the only prime sandwiched between a prime and a

composite number.

http://primes.utm.edu/curios/page.php/3.html

3 is the only prime followed by a square.

http://mathworld.wolfram.com/Near-SquarePrime.html

Every positive integer is the sum of at most 3 triangular

numbers.

http://mathworld.wolfram.com/TriangularNumber.html

4 is the smallest number of colors sufficient to color all

planar maps.

http://en.wikipedia.org/wiki/Four_color_theorem

4 is the only positive number that is both the sum and the

product of the same two integers.

http://www.answerbag.com/q_view/675826

Are you sure that 2 plus 2 is equal to 2 times 2?

Answer

by "Yarnlady is happy every day" on April 6th, 2008

Let's see: here's two xx

and here's two more xx

So how many times did I put two xx on the page? Two times.

so xx plus xx is 4 (xxxx)

and two times xx is (goes back and counts them xx xx)

Wow, 4.

4 is the order of the smallest non-cyclic group (submitted by

Sam Steingold).

http://en.wikipedia.org/wiki/List_of_small_groups

Every positive integer is the sum of at most 4 squares.

http://en.wikipedia.org/wiki/Waring%27s_problem

4 is the only composite number that is equal to the sum of

its prime factors.

http://www.wordiq.com/definition/Four

4 is the only composite number n which doesn't divide (n-1)!

http://www.physicsforums.com/archive/index.php/t-349819.html

5 is the number of Platonic solids.

http://en.wikipedia.org/wiki/Platonic_solid

6 is the smallest perfect number.

http://en.wikipedia.org/wiki/Perfect_number

6 is the order of the smallest nonabelian (non commutative)

group.

http://en.wikipedia.org/wiki/List_of_small_groups

7 is the smallest number of faces of a regular polygon that

is not constructible by straightedge and compass.

http://en.wikipedia.org/wiki/Constructible_polygon

8 is the largest cube in the Fibonacci sequence.

http://mathoverflow.net/questions/1624/is-8-the-largest-

cube-in-fibonacci-sequence

9 is the maximum number of cubes that are needed to sum to

any positive integer.

http://en.wikipedia.org/wiki/Waring%27s_problem

9 is the smallest odd positive composite integer.

http://www.numbergossip.com/9

10 is the base of our number system.

http://ideonexus.com/2008/07/08/why-a-base-10-number-system/

10 is the smallest product of two non-consecutive primes.

Contributed by Cris Stringfellow