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 2006-02-16, 17:11 #1 davar55     May 2004 New York City 10000100010112 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.
 2006-02-19, 10:38 #2 nibble4bits     Nov 2005 B616 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.
 2006-02-20, 01:33 #3 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101ร103 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".
2006-02-20, 03:26   #4
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22·33·19 Posts
Geometry Puzzle

Quote:
 Originally Posted by davar55 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.
Think in terms of angles.
The number two represents 2*pi which the circle contains
The number 1 pi for a straight line.
Mally

 2006-02-23, 06:34 #5 nibble4bits     Nov 2005 B616 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.
 2009-07-02, 19:24 #6 davar55     May 2004 New York City 5×7×112 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 .....................
2009-07-02, 19:37   #7
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101ร103 Posts

2A8F16 Posts

Quote:
 Originally Posted by davar55 The answer I intended was:
I got that in my alternate solution.

 2009-07-02, 19:41 #8 davar55     May 2004 New York City 5×7×112 Posts Well, didn't you ever think to extend and improve the original puzzle? Aren't you interested in Math?
2009-07-05, 10:53   #9
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

2×73×17 Posts

Quote:
 Originally Posted by davar55 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 .....................
Trivial. A point has only an outside.

Paul

2009-07-05, 20:02   #10
davar55

May 2004
New York City

10000100010112 Posts

Quote:
 Originally Posted by xilman Trivial. A point has only an outside. Paul
Yes, so the answer to my puzzle,
going in the opposite direction,
is that a point has one side.

So what geometric shape has zero sides,
and how about minus one and two?

2009-07-06, 06:28   #11
10metreh

Nov 2008

2×33×43 Posts

Quote:
 Originally Posted by davar55 Yes, so the answer to my puzzle, going in the opposite direction, is that a point has one side. So what geometric shape has zero sides, and how about minus one and two?
-1 and -2: a point and a circle constructed from antimatter.

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