Hexagon

GinoJ

Posers and Puzzles

20 Feb 07 19:41

FabianFnas

Joined: 11 Nov 05
Moves: 43938

20 Feb 07 21:20

1 edit

Originally posted by GinoJ
Hey Fabian, life too short to get angry brotha'.

No no, I'm not angry - if you just tell me the glitch?

If I ask you the same question to you, but now with the Area of a regular heptagon with each side being 1 cm in length, what will be your answer?

This one is exclusively for Gino. Just so he might show off and prove that he knows what he's talking about. Do you have enough math, Gino?

GinoJ

Joined: 20 Jan 07
Moves: 1005

21 Feb 07 05:11

1 edit

Originally posted by FabianFnas
No no, I'm not angry - if you just tell me the glitch?

If I ask you the same question to you, but now with the Area of a regular heptagon with each side being 1 cm in length, what will be your answer?

This one is exclusively for Gino. Just so he might show off and prove that he knows what he's talking about. Do you have enough math, Gino?

I do not think I could ever have as much as yours. 😉

[edit] So, I leave the "posers and puzzles" section to your dominance since I am just an ignorant. 😠

Have fun!

FabianFnas

Joined: 11 Nov 05
Moves: 43938

21 Feb 07 07:06

Originally posted by GinoJ
I do not think I could ever have as much as yours. 😉

[edit] So, I leave the "posers and puzzles" section to your dominance since I am just an ignorant. 😠

Have fun!

If you leave, Gino, much of the recent fun goes with you.
This fourm is very dependant of people who invent or copy problems so the rest of us put the little grey ones in ction.

One problem is better than no problem, even if a good problem is better than an ordinary one. And favorites is always welcome if they're good.

The way of solving the heptagon problem could be very like that of the hexagon. Give it a try and see where it leads.

geepamoogle

Joined: 15 Feb 07
Moves: 667

21 Feb 07 07:39

A heptagon has 7 sides, does it not? I daresay the answer to your query will end up a great deal more complicated than the previous question, because it will involve trigonometry, and the sines and cosines of angles which have no exact answer, only approximations.

With a hexagon, you were dealing with sin(60d) which is very well known as an exact number (sqrt(3)/2)

The area of a heptagon would be 3.5 * sin(64+2/7d).

mtthw

Joined: 07 Sep 05
Moves: 35068

21 Feb 07 12:58

1 edit

It's not too hard to extend it to a regular polygon with n sides (for n > 2).

You can break it down into n isosceles triangles with a base or length 1 and a height of 1/[2tan(180/n)]

So the area = n/[4tan(180/n)]

(As a check, put in n = 4 and you get A = 1 as expected)

sonhouse

Fast and Curious

slatington, pa, usa

Joined: 28 Dec 04
Moves: 53419

21 Feb 07 18:16

1 edit

Since a regular hexagon is composed of 6 equalateral triangles you can just solve for the area of one triangle and multiply by 6:
A=Sqr root of (S*(S-a)*(S-b)*(S-c)
a, b and c all = exactly 1.
S= (a+b+c)/2
S= 3/2
S= 1.5
So, Sqr root of (1.5)*(0.5)*(0.5)*(0.5) = Sqr root (1.5)*(0.125)
= Sqr root of (0.1875) or 0.433012702 = area of equalateral triangle of side 1.
0.433012702 * 6= 2.598076211 Square units= area of regular hexagon with unit sides. So 2.59 and change is the answer.
I deliberately did it a differant way from Fabian and got exactly the same answer so what is wrong with YOUR logic?