Sagitta method

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Derivation of the Sagitta method

The Sagitta method makes it possible to determine a circle radius using a section of a circle . This is always useful when the entire image of a circle is not available.

With the Sagitta method, two points ( and ) on a circular line are marked and the length of the resulting circular tendon is determined. Then a vertical line is drawn at the center of the chord and the height of the circle segment is determined. The unknown radius from point to forms a right triangle with the difference and . Using the Pythagorean theorem , the following can be calculated from the measurements:

The transformation

and expanding with and

after further forming delivers:

Historically, the height of the circle segment was referred to as the sagitta and the distance between the tendon and the center of the circle as the apothema .


Individual evidence

  1. Floria Naumann: Use of bubble chamber images in schools on an increased requirement level. 2.2.3 Geometric reconstructions with the recordings. TU-Dresden, September 10, 2015, p. 21 , accessed on January 14, 2019 .