Method for equally dividing circumference
A technology of circle and bisector, applied in the field of drawing, can solve the problems of n equal division and known arc n equal division which cannot be theoretically realized.
Inactive Publication Date: 2016-02-03
郭保德
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Problems solved by technology
For these problems, in the existing drawing tools (including software tools), any single tool or combination of tools cannot theoretically realize arbitrary n equal divisions, only part of them can be realized, for example, when n=2n, 3, 4, 5 and a few can be realized
[0003] For n (natural number) equal division of the circumference, there is no theoretical or practical operation that can divide a known circle n (natural number) equally; similarly, there is no theory or actual operation that can divide a known circle Arc n (natural number) is equally divided; similarly, there is no theory or practical operation that can divide a known angle n (natural number) equally
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[0016] The present invention will be further described below in conjunction with accompanying drawing:
[0017] Principle analysis of the present invention:
[0018] Since the circumference of a known circle is equal to 2πr (where r is the radius of the known circle); the n equal divisions of the known circle, that is, the n equal divisions of the known circle's circumference (2πr), That is to say, each arc divided by n is equal to 2πr / n; we regard 2πr / n as the product of 2π and r / n, and according to the circumference of a circle equal to 2πr, then: the circumference of a known circle (2πr) is A circle composed of n circles whose radius is r / n, that is, n×{2π(r / n)}=2πr. It can be understood as: n circles with a radius of r / n roll along the perimeter of a known circle, and the trajectory formed on the known circle can also be understood as: a circle with a radius of r / n is the trajectory formed by rolling n circles of a circle with a radius along the perimeter of a known circ...
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The invention provides a method for equally dividing a circumference. A new tool deformed and improved on the basis of an existing common drawing tool is utilized, the circumference with the radius of r / n is rolled on the perimeter of a circumference with the known radius of r by n circles, a point is marked every time the circumference is rolled by one circle, and therefore the equal division points of the known circumference are found, and the known circumference is equally divided into any n parts, wherein n is a natural number. The mathematical problem of equally dividing the known circumference into any n parts is solved, and errors are avoided in theory. Meanwhile, the problems that a known arc and a known angle are equally divided into any n parts, a n-regular polygon is drawn in a known round, an externally tangent n-regular polygon is drawn in the known round, the position of phi is drawn on a number axis, and the round with the know perimeter is drawn out are solved. The angle measurement mode is changed, the theoretic 1 / n degree can be drawn out, n can be any natural number, and the process cannot be achieved by a protractor.
Description
technical field [0001] The invention belongs to the technical field of drawing, and relates to a drawing method for performing arbitrary n (natural number) equal divisions on a known circle, in particular to a method for equally dividing the circle. Background technique [0002] At present, in the fields of scientific research, teaching, surveying and mapping, mechanical engineering, etc., it often involves n equal divisions of a known circle, or n equal divisions of a known angle or arc, and doing it in a known circle. Inscribed regular n-gon, or circumscribed n-gon, etc. For these problems, in the existing drawing tools (including software tools), any single tool or combination of tools cannot theoretically realize arbitrary n equal divisions, only part of them can be realized, for example, when n=2n, 3, 4, 5, etc. a few can be achieved. [0003] For the n (natural number) equal division of the circumference, there is no theoretical or practical operation that can divide...
Claims
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IPC IPC(8): B43L13/00
Inventor 郭保德郭健
Owner 郭保德