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  2. Rule of thirds - Wikipedia

    en.wikipedia.org/wiki/Rule_of_thirds

    The horizon in the photograph is on the horizontal line dividing the lower third of the photo from the upper two-thirds. The tree is at the intersection of two lines, sometimes called a power point [1] or a crash point. [2] The rule of thirds is a rule of thumb for composing visual art such as designs, films, paintings, and photographs. [3]

  3. 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.

  4. Dividing a square into similar rectangles - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_square_into...

    However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...

  5. Angle trisection - Wikipedia

    en.wikipedia.org/wiki/Angle_trisection

    The triple-angle formula gives an expression relating the cosines of the original angle and its trisection: cos θ = 4 cos 3 ⁠ θ / 3 ⁠ − 3 cos ⁠ θ / 3 ⁠. It follows that, given a segment that is defined to have unit length, the problem of angle trisection is equivalent to constructing a segment whose length is the root of a cubic ...

  6. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    To divide a fraction by a whole number, you may either divide the numerator by the number, if it goes evenly into the numerator, or multiply the denominator by the number. For example, 10 3 ÷ 5 {\displaystyle {\tfrac {10}{3}}\div 5} equals 2 3 {\displaystyle {\tfrac {2}{3}}} and also equals 10 3 ⋅ 5 = 10 15 {\displaystyle {\tfrac {10}{3\cdot ...

  7. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, nor would either truly be 13x5 if it were, because what appears to be the hypotenuse is bent. In other words, the "hypotenuse" does not maintain a consistent slope , even though it may appear that way to the human eye.

  8. List of formulas in elementary geometry - Wikipedia

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

    The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

  9. Chord (geometry) - Wikipedia

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

    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"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse.

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