OT: In need of a math whiz

[Jody]

Ok, here is the challenge.

A rug is in the shape of an octagon and measures 7'10 across.

How many inches in length is each of the 8 sides?

[Michele Jackson]

And the answer is: 35.97 inches.

(seriously)

[Jody]

GET. OUT.!!!!

[Jody]

We are going to need to see your work!

[Michele Jackson]

A circle divided into 8 segments yields 8 triangles. Each of those triangles is an isoscoles triangle with two sides of 47" long, one angle of 45 degrees and two angles of 67.5 degrees. You want to know the length of the third side. If you split the triangle into two smaller triangle each with a 90 degree angle then you can use the sine, cosine rules.

To double-check the answer you can also determine the overall circumference of the circle using 2*pi*r and divide it by 8. That yields 36.9 with is slightly larger than than 35.97, which makes sense.

Got it?

[DMG]

I got 38.94" but that's not measuring from corner to corner across the octogon; that's measuring from flat to flat as if you were measuring the height of a stop sign. I guess the real answer is a smidgen over three feet.

Cheers!

~Dave

[Clif]

Ohhhhh yeah... clear as a bell..... :roll:

[Fish]

Well, Michelle's description is great - way to not just memorize the polygon formulae back in school Michelle! She goes after it using only basic geometry, which everyone remembers from junior high, right? :-) And her check on the answer for reasonableness is an excellent last step. Just like we teach it in school!

You do have to know if the 7'10" across means across the diagonal or from the center of one side to the center of the opposite side. In the former case, the 7'10" is twice the radius of the octagon. In the second, it's twice the apothem. Apothem is a Latin term that translates as "only math teachers can remember this word."

Former geometry teacher,
Fish

[DMG]

You see what you mad me do on my day off! If you had caught me 20 years ago, I'm certain I could have done this with only one sheet of paper . Cheers!

[Fish]

You see what you mad me do on my day off! If you had caught me 20 years ago, I'm certain I could have done this with only one sheet of paper . Cheers!

Showing that there's more than one way to skin the polygon perimeter cat!

[DMG]

Apothem? Never heard that one. If you ask me, the sides are apothemately three feet. Can we have some rain?

[scoutdad]

sin45(47)=33.24

But my trig is very rusty.

yes we do need some rain

[Jody]

This is freakin' hilarious.




Good Job, Meesh.

[Michele Jackson]

OK - Fish brings up a good point. I calculated using the apothem. (not that I recall ever hearing that word before). My calculations were based on the diagonal measurement. If I assume the 7'10" is the straight across measurement I come up with 38.9", same as DMG. What do you get Fish?

Goss I wish it would rain!

[DMG]

I propose a new mathematical term for the ratio of the length of the sides of an octagon fitted the outside of a circle over the length of the sides of an octagon fitted to the inside of the same circle:

Outside length/inside length = 38.94/35.97 = 1.08257

We'll call it Jody's Constant!

J = 1.08257

Now, about that rain?