# Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

@inproceedings{Brummelen2012HeavenlyMT, title={Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry}, author={Glen van Brummelen}, year={2012} }

Preface vii 1 Heavenly Mathematics 1 2 Exploring the Sphere 23 3 The Ancient Approach 42 4 The Medieval Approach 59 5 The Modern Approach: Right- Angled Triangles 73 6 The Modern Approach: Oblique Triangles 94 7 Areas, Angles, and Polyhedra 110 8 Stereographic Projection 129 9 Navigating by the Stars 151 Appendix A. Ptolemy's Determination of the Sun's Position 173 Appendix B. Textbooks 179 Appendix C. Further Reading 182 Index 189

#### 99 Citations

On Cesàro triangles and spherical polygons

- Mathematics
- 2021

In Donnay’s and Van Brummelen’s monographs on spherical trigonometry, the Cesaro method is revitalized to derive various results on spherical triangles. Using Cesaro’s triangles, we derive in this… Expand

Spherical Trigonometry in the Islamic World

- Geography
- 2016

The problems of spherical trigonometry concern the sizes of circular arcs or angles on the surface of a sphere, and their relationships to each other. In applications, the sphere was either the… Expand

Lexell’s theorem via stereographic projection

- Physics
- 2018

Lexell’s theorem states that two spherical triangles $$\triangle {ABC}$$▵ABC and $$\triangle {ABX}$$▵ABX have the same area if C and X lie on the same circular arc with endpoints which are the… Expand

Napier, Torporley, Menelaus, and Ptolemy: Delambre and De Morgan’s Observations on Seventeenth-Century Restructuring of Spherical Trigonometry

- 2016

An effort to reorganize and systematize planar and spherical trigonometry began in the 15th century with the work of Regiomontanus, extended throughout the 16th century with work by Otho, Rheticus,… Expand

Stereographic Trigonometric Identities

- Computer Science, Mathematics
- Am. Math. Mon.
- 2015

Abstract We show that trigonometric identities arising from the most well known alternative to the arc-length parametrization of the circle share some of the same elaborate nature as the more… Expand

Micha lMusielak DIAMETER OF REDUCED SPHERICAL CONVEX BODIES

- 2019

The intersection L of two different non-opposite hemispheres of the unit sphere S is called a lune. By ∆(L) we denote the distance of the centers of the semicircles bounding L. By the thickness ∆(C)… Expand

On the Trigonometric Correction of One Powerful Formula

- Physics
- 2015

An attempt is presented for the description of the magnitude of Newton’s gravitational force in the experiments with a horizontal torsion balance. There were developed many experimental arrangements… Expand

The Rise of “the Mathematicals”: Placing Maths into the Hands of Practitioners—The Invention and Popularization of Sectors and Scales

- Engineering
- 2015

Following John Napier’s invention of logarithms in 1614, the remainder of the sixteenth century saw an explosion of interest in the art of mathematics as a practical and worldly activity. Mathematics… Expand

On the Hidden Beauty of Trigonometric Functions

- Physics
- 2017

In the unit circle with radius R = E 0 = mc 2 = 1 we have defined the trigonometric function cos(Theta) = v/c. The known trigonometric functions revealed the hidden relationships between sensible… Expand

Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes

- Mathematics
- 2019

After a few claims about lunes and convex sets on the d -dimensional sphere $$S^d$$ S d we present some relationships between the diameter, width and thickness of reduced convex bodies and bodies of… Expand