# Math Challenge

• Feb 9th 2006, 02:32 PM
lil_josh
Math Challenge
This is a challege my teacher gave to me and i just cant figure it out. Can anyone help me on this one?

A circle of radius 1 inch is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex, tangent to the circle and to two sides of the triangle. If this process is continued indefinetly, what is the SUM of the circumferences of all the circles?
• Feb 9th 2006, 03:09 PM
CaptainBlack
Quote:

Originally Posted by lil_josh
This is a challege my teacher gave to me and i just cant figure it out. Can anyone help me on this one?

A circle of radius 1 inch is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex, tangent to the circle and to two sides of the triangle. If this process is continued indefinetly, what is the SUM of the circumferences of all the circles?

Its infinite. That is if you assume that you are adding extra sides to form smaller
triangle associated with your new circles at each stage.

The circumference of the new circles at each stage is one third of the
circumference at the stage before, but there are three times as many
so at each stage we are adding the same increment to the total circumference.

RonL
• Feb 9th 2006, 03:14 PM
lil_josh
WOW! I never would of got that. Good job man!
• Feb 9th 2006, 05:51 PM
ThePerfectHacker
This reminds me of fractals.
• Feb 10th 2006, 03:07 AM
CaptainBlack
Quote:

Originally Posted by lil_josh
WOW! I never would of got that. Good job man!

Don't just accept what I say, check that you agree with what I
have said. We all can meke mistakes :)

RonL
• Feb 10th 2006, 04:09 AM
lil_josh
Alright I'll try it.