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How did Willebrord Snell use triangles to survey part of the Netherlands?
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trigonometry
Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.
Willebrord Snell, a Dutch mathematician and astronomer, pioneered the use of triangulation as a scientific method to measure the size of the Earth, an achievement he detailed in his 1617 work Eratosthenes Batavus.12
To survey part of the Netherlands, Snell established a network of 33 connecting triangles. The process involved the following steps:2
- Baseline Measurement: He measured one side of the initial triangle, known as the baseline, with high precision.32
- Angle Measurement: Using instrumental triangulation, he measured the angles of the triangles in the chain.42
- Trigonometric Calculation: By applying the law of sines, he computed the lengths of the remaining sides of the triangles based on the known baseline and measured angles.2
By constructing this chain of triangles, Snell was able to determine the length of a meridian arc. Although his final calculation for the size of the Earth was approximately 3.4 percent too small, his development of triangulation as a systematic surveying technique laid the foundation for modern geodetic measurements.42