Geometry Puzzle

[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.

[nibble4bits]

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.

[Uncwilly]

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".

[mfgoode]

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

[nibble4bits]

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.

[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 .....................

[Uncwilly]

Originally Posted by davar55

The answer I intended was:

I got that in my alternate solution.

[davar55]

Well, didn't you ever think to extend and improve the original puzzle?

Aren't you interested in Math?

[xilman]

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

[davar55]

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?

[10metreh]

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.