Why the circle can not be divided in seven parts?

Question

Well, even if you construct a heptagon, and you divide that way, there is an error. Angle is 51.428571 and period is repeting "428571". So we dont have 100% sure division of a circle. Do you have an idea? This is a centuries and centuries old problem, Karl F. Gauss and Kepler also. If you say Circumference is 21, and divided by 7 would be 3 then diametar of that circle is 2.228169203286535

http://www.geocities.com/antidummy/sub/measurement.html

http://www.geocities.com/robinhuiscool/heptagon.html

http://www.broug.com/polygons.html

http://math.about.com/library/blcirclecalculator.htm

Answer 1

I see the same question for the second time. I have answered already some 1 hour ago, look there, but I must repeat: the question must be precisely formulated - what do we mean exactly by "to divide a circle in 7 equal parts"?
If we mean to find the length of each arc - there is no problem, the answer is 2*pi*R/7 (R-radius);
If we mean to find the angle each arc contains - again there is no problem - 360°/7;
If we mean to find the side length of the inscribed heptagon - again easy - 2*R*sin(360°/14);
But if we wish to CONSTRUCT with classical instruments (ruler and compass) that angle or that side, that's impossible (proven by Gauss in the beginning of 19th century). The constructions in the websites, cited above are APPROXIMATE!

P.S.(Edit) See also Wikipedia, articles "Constructible polygons", "Fermat number"

Answer 2

If the circumference of a circle is rational, the diameter will *always* be irrational.

Construct a heptagon. Drop lines from the midpoint of each side to the opposite vertex. All seven of the lines will intersect at the center of the circle. Place your compass with the sharp point at the center, and the scribing point at one of the vertices, and draw the circle.

Are the angles nice little numbers? No. Is the diameter a nice little circle? No. But the circle can be divided in seven parts, ANYWAY.

Answer 3

the simple answer would be because you cannot divide 360 (the number of degrees in the circle) evenly into 7
this can be done with all the other numbers through ten
360/1=360
360/2=180
360/3=120
360/4=90
360/5=72
360/6=60
360/7=51.4
360/8=45
360/9=40
360/10=36

Answer 4

For fair accuracy, use radius 15 and chord length 13. For better accuracy, use radius 53 and chord length 46. Better yet, radius 121, chord 105.