20060216, 17:11  #1 
May 2004
New York City
1000010001011_{2} Posts 
Geometry Puzzle
What is the pattern in the following list?
The number "6" within a regular hexagon; The number "5" within a regular pentagon; The number "4" within a square; The number "3" within an equilateral triangle; The number "2" within a circle. 
20060219, 10:38  #2 
Nov 2005
B6_{16} Posts 
The 2 for circle is funny  Everyone expects to see infinite or a line.
The circumference of a circle is the radius times Pi but the units of measurement for the full circle is 2 times Pi. If you substituted 1 for the radius then you'de expect them to use Pi for 360 degrees. There's a reason that they do this! I'll let others look this up before explaining my reasoning along those lines. Now as for why it's a circle at 2, I can argue that you chose a shape that has either 1(geometric intuition) or infinite(geometric calculus) sides depending on how you look at it. I think you chose another way to compare these shapes besides the number of sides. ;) The perimeter of the circle is Pi*r, the perimeter of the triangle is 3 times the width of any side. http://www.efunda.com/math/areas/RegularPolygonGen.cfm has some other formulas. I was wondering if this is a good approach. 
20060220, 01:33  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
5·2,179 Posts 
Minimum number of points to define the shape. The polygons have the vertices, the circle has the center and a point on the circle.
Alternately: The number of sides. The polygons are obivous, while the circle has the in"side" and the out"side". 
20060220, 03:26  #4  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Geometry Puzzle
Quote:
The number two represents 2*pi which the circle contains The number 1 pi for a straight line. Mally 

20060223, 06:34  #5 
Nov 2005
B6_{16} Posts 
LOL
I thought of the inside and outside but that just means the nth polygon has 2n number of sides by that definition. I think the idea of the number of points has to be a good answer. 
20090702, 19:24  #6 
May 2004
New York City
5×7×11^{2} Posts 
Sorry about our deceased "gadfly" mfgoode.
His answer may contain an iota of truth. The answer I intended was: A hexagon has 6 sides. A pentagon has 5 sides. A square has 4 sides. A triangle has 3 sides. A circle has 2 sides, an inside and an outside (hahaha). I remember this puzzle from long ago. Try extending it upwards. If you're really good, try extending it downwards. Enjoy ..................... 
20090702, 19:37  #7 
6809 > 6502
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Aug 2003
101ร103 Posts
2A8F_{16} Posts 

20090702, 19:41  #8 
May 2004
New York City
5×7×11^{2} Posts 
Well, didn't you ever think to extend and improve the original puzzle?
Aren't you interested in Math? 
20090705, 10:53  #9  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×7^{3}×17 Posts 
Quote:
Paul 

20090705, 20:02  #10 
May 2004
New York City
1000010001011_{2} Posts 

20090706, 06:28  #11 
Nov 2008
2×3^{3}×43 Posts 

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