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Unlike degrees, radians have a more mathematical background. Science History Publications, New York, 1977. The Sea Island Mathematical Manual: surveying and mathematics in ancient China. The full text of this interesting and inspiring talk is online at http://www.ima.umn.edu/newsltrs/updates/summer03 Asking "What makes the math sciences so central?", he answers by quoting Galileo: "The great book of nature can be read only by those who know the language in which it was written.
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A sphere is a solid such that any point on its surface is the same distance from a point within, called the centre. The following terms are used in practical applications of geometry and trigonometry. Suppose that a surveyor, standing at 0 (Fig. 35) wishes to determine the height of a distant tower and spire. His first step would be to place a telescope (in a theodolite) horizontally at O On the represenation of a function by a trigonometric series
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. This treatise later had a "strong influence on European mathematics", and his "definition of ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus.  The method of triangulation was first developed by Muslim mathematicians, who applied it to practical uses such as surveying  and Islamic geography, as described by Abu Rayhan Biruni in the early 11th century Precalculus with Trigonometry: Concepts and Applications, Teacher's Edition
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