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  2. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. [1] Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter.

  3. String girdling Earth - Wikipedia

    en.wikipedia.org/wiki/String_girdling_Earth

    Surprisingly, the answer is 2 π m or around 6.3 metres (21 ft). In the second phrasing, considering that 1 metre (3 ft 3 in) is almost negligible compared with the 40,000 km (25,000 mi) circumference, the first response may be that the new position of the string will be no different from the original surface-hugging position.

  4. Tree girth measurement - Wikipedia

    en.wikipedia.org/wiki/Tree_girth_measurement

    The Tule tree has a diameter of 38 feet 1.4 inches (1,161.8 cm) as measured by tape wrap, but because of its irregularity a cross-sectional wood area expressed as a circle gave an effective diameter of only 30 feet 9 inches (937 cm). The base of the tree was mapped in three dimensions using a frame mapping technique.

  5. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    Given three points A, B and C on a circle with center O, the angle ∠ AOC is twice as large as the angle ∠ ABC. A related result to Thales's theorem is the following: If AC is a diameter of a circle, then: If B is inside the circle, then ∠ ABC > 90° If B is on the circle, then ∠ ABC = 90° If B is outside the circle, then ∠ ABC < 90°.

  6. 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.

  7. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    Circle with similar triangles: circumscribed side, inscribed side and complement, inscribed split side and complement. Let one side of an inscribed regular n-gon have length s n and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter.

  8. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    Circumference: the length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest ...

  9. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, [1] in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like a honeycomb), and each circle is surrounded by six other circles. For circles of ...