# 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 thisExpand
Spherical Trigonometry in the Islamic World
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 theExpand
Lexell’s theorem via stereographic projection
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 theExpand
Napier, Torporley, Menelaus, and Ptolemy: Delambre and De Morgan’s Observations on Seventeenth-Century Restructuring of Spherical Trigonometry
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
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 moreExpand
Micha lMusielak DIAMETER OF REDUCED SPHERICAL CONVEX BODIES
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
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 arrangementsExpand
The Rise of “the Mathematicals”: Placing Maths into the Hands of Practitioners—The Invention and Popularization of Sectors and Scales
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. MathematicsExpand
On the Hidden Beauty of Trigonometric Functions
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 sensibleExpand
Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes
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 ofExpand