You are here:
- Home
- Science
- Mathematics
- Advanced Math
- dividing circles
Advanced Math/dividing circles
Advertisement
Question
My 8-year old son wants to know if 360 is the maximum number of pieces a circle can be divided into. (equally). I think the maximum number is 360, he thinks the maximum number is infinite. Could you explain (simply if possible) the answer? Thank You!!!!!
As usual, our children tend to be right.
Divide a circle into 360 pieces, 1° each.
Cut each in half, and now you have 720 pieces, each with 1/2°
Cut each of these in half, and now you have 1,440 pieces, each with 1/4°.
Keep cutting each of them in half, and the problem will give us however many pieces we want. The result is seen that there is no end to how many pieces you can divide a circle into if it's thought about. Now doing this on paper, the width of a line would quicly be wider than the section of circle, even with a big circle and a find tip writing utensil.
Note that the divisions don't half to be linear and you could divide a circle any way that was desired to get the number of pieces it is suppose to have.
For example, to get three pieces, you might chop it in half and then chop one side in half, so the areas of each one would be 1/2, 1/4, and 1/4 of the whole.
If the other side was chopped into three pieces, the entire circle would then have 5 secitons. 3 of the sections would be 1/6th of the total area and 2 of the sections would be 1/4 of the total area.
This is to show that the total of all of the areas is 1 entire circle, for 1/6 + 1/6 + 1/6 + 1/4 + 1/4 = 1/2 + 1/2 = 1 entire circle.
I'm not sure how to divide a circle into n equal pieces, but it can be divided into two pieces by cutting it in half. It can be divided into one more piece by drawing a straight line from the center to and edge. This can be done in theory indefintely.
Related Articles
Answers by Expert:
Scott A Wilson
Expertise
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?
Experience
Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later.
I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman.
I tutored at Mathnasium for well over a year.
I worked at The Boeing Company for over 5 years.
I received an MS degreee in Mathematics from Oregon State Univeristy.
The classes I took were over 100 hours of upper division credits in mathematical courses such as
calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more.
I graduated with honors in both my BS and MS degrees.
Past/Present Clients: College Students at Oregon State University, various math people since college,
over 7,500 people on the PC from the US and rest the world.
Publications
My master's paper was published in the OSU journal.
The subject of it was Numerical Analysis used in shock waves and rarefaction fans.
It dealt with discontinuities that arose over time.
They were solved using the Leap Frog method.
That method was used and improvements of it were shown.
The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.
Education/Credentials
Master of Science at OSU with high honors in mathematics.
Bachelor of Science at OSU with high honors in mathematical sciences.
This degree involved mathematics, statistics, and computer science.
I also took sophmore level physics and chemistry while I was attending college.
On the side I took raquetball, but that's still not relevant.
Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State.
I was in near the top in most of my classes. In several classes in mathematics, I was first.
In a class of over 100 students, I was always one of the first ones to complete the test.
I graduated with well over 50 credits in upper division mathematics.
Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions,
and several people every day on the PC, and you're probably make one more.
©2012 About.com, a part of The New York Times Company. All rights reserved.