How do I split a circle in 12 equal pieces, without a protractor?

Question

...or any other amount of pieces.

Answer 1

1. Find the center of the circle.
2. Set your compass to the radius of the circle.
3. Pick one point on the circumference of the circle and use your compass to divide the circumference into six equal pieces.
4. Draw those six radii.
5. Bisect each one of those angles. (Or bisect just one of the angles and then transfer that angle to the other sixths.

As for the "any other amount" part...
Each division of a circle is different. For instance, dividing a circle into fifths is possible, but it is nothing like this method for twelveths.

Mesocyclone,
Trisecting an angle... You, sir, are a dog. :-)

Answer 2

"any other amount of pieces" ... there are limitations in the number if you restrict to "compass and straightedge", thre "classical tools" which have been subjected to mathematical analysis over hundreds / thousands of years


for instance you can't make a 7-sided regular polygon

cite :
In 1796, at the age of 19, Gauss have shown that a regular heptadecagon (a 17-sided polygon) is constructible. As Gauss showed, the heptadecagon was only a particular case of a family of constructible regular polygons. Any N-gon, where N is in the form 2np1...pm, where pi's are distinct Fermat primes (i.e. primes in the form [2^2^k ]+ 1), is constructible.
end-cite



n a positive integer >1

you can do "n" equal-area pieces if you divide a diameter into n-equal length segments ... call the points bracketing these segments "p0, p1, p2, ... pn" ... and thier midpoints "m1, m2, m3, ... mn" [note that each segment has a unique midpoint]


.

geeze, take the case n=4:
plaCE COMPASS AT MIDPOINT OF FIRST SEGMENT AND DRAW A SEMI-CIRCLE RADIUS1/4 THE RADIUS OF ORIGINAL CIRRCLe "above" the diameter

next place the compass pivot-point at the midpoint of th 3rd segment and draw semilcircle with raius = 3/4 the original circle "below" the diameter

... sheesh, typing descriptions is cumbersome

.....

place pivot point at point p1 ... arrrgh, no time

it the "generalized yin-yang" symbol [n=2]

semi-circels radius k/n and (n-k)/n for k = 1 to n-1
above and below the diameter ..

Answer 3

You cannot trisect an arbitrary arc, but within a 90° angle, you can. To get 12 sections, quarter the circle, then trisect each one.

I can't explain exactly how to perform the trisection. This sounds like an extra credit problem, so you should figure it out yourself.

Answer 4

divide the circle into 6 equal parts, and bisect them

Answer 5

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Cut the circle in half and cut wedges from every 30 degree arc.

Answer 6

Use a ruler but it probaly won't be squares....try thinking of diffrent other shapes(because a cirlce with equal squares is very hard

Answer 7

Divide the circle into fourths, then those fourths into thirds.

Answer 8

Think "clock"