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#1 2014-05-02 15:44:07

Sven
Member
Registered: 2014-05-02
Posts: 18

Polygonal numbers

I had this from Euler's Algebra proof to represent polygonal numbers of any kind but I don't understand what it means it goes like this:
Draw a polygon haing number of sides required n this number is constant for the whole series n equal to 2 + diff of arith progress
Then choose on of its angles n draw diagonals n the sides of he angle n the diagonal are to be indefinetly produced
After that I take these 2 sides n diagonals o he first polygon as I often as I choose n draw from corresponding points marked by compass lines parallel to first polygon n divide them in as many equal parts or as many points as there are actualy in the diagonals in the 2 sides produced.
Please give geometrical represantation of the proof if you can
God bless n thank you

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#2 2014-05-02 20:24:36

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Polygonal numbers

hi Sven,

Welcome to the forum.

I had not learnt of polygonal numbers so I had to look it up.  There is a good article here:

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

I cannot follow exactly what you are describing but you can build a formula like this:

Diagram below (from Wiki and modified).  Here n = 6.

The table shows a column for differences where the differences are n - 2 (= 4)

The second column is an arithmetic progression with first term, a = 1, and common difference, d  = n-2

Terms in arithmetic progressions are given by t = a + (m-1)d

The third column shows the polygonal numbers.  Each number = previous number + next term in the ap.

So you can build the formula from this.

Hope this helps.  Post again, smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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