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The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Specifically, draw a diagonal line connecting two points on the diagram so that every other point is either on or to the right and above it. There is at least one such line if the curve passes through the origin. Let the equation of the line be qα+pβ=r. Suppose the curve is approximated by y=Cx p/q near the origin.
The simplest method of drawing a line involves directly calculating pixel positions from a line equation. Given a starting point (,) and an end point (,), points on the line fulfill the equation = +, with = = being the slope of the line. The line can then be drawn by evaluating this equation via a simple loop, as shown in the following pseudocode:
More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT 'Connections’ hints and answers for #586 on Friday ...
It is relatively straightforward to construct a line t tangent to a circle at a point T on the circumference of the circle: A line a is drawn from O, the center of the circle, through the radial point T; The line t is the perpendicular line to a. Construction of a tangent to a given circle (black) from a given exterior point (P).
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