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  2. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    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.

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities

  4. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    where a is the radius of the circle, (,) are the polar coordinates of a generic point on the circle, and (,) are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of ...

  5. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    The transformation sends the circle to an ellipse by stretching or shrinking the horizontal and vertical diameters to the major and minor axes of the ellipse. The square gets sent to a rectangle circumscribing the ellipse. The ratio of the area of the circle to the square is π /4, which means the ratio of the ellipse to the rectangle is also π /4

  6. Pentagon - Wikipedia

    en.wikipedia.org/wiki/Pentagon

    Draw a circle centered at M through the point A. Mark its intersection with the horizontal line (inside the original circle) as the point W and its intersection outside the circle as the point V. Draw a circle of radius OA and center W. It intersects the original circle at two of the vertices of the pentagon. Draw a circle of radius OA and ...

  7. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.

  8. Lune of Hippocrates - Wikipedia

    en.wikipedia.org/wiki/Lune_of_Hippocrates

    The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.

  9. Squaring the circle - Wikipedia

    en.wikipedia.org/wiki/Squaring_the_circle

    Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by using only a finite number of steps with a compass and straightedge .

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