To refine search, see subtopics Karl Friedrich Gauss (1777-1855) and August Ferdinand Möbius (1790-1868). To expand search, see Germany and The 1800s. Laterally related topics: Germany in the 1600s, Germany in the 1500s, Germany in Ancient Times, Germany in the 1700s, Germany in the 1900s, Austria in the 1800s, and Hungary in the 1800s.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Hansen, David W. The Dependence of Mathematics on Reality. Mathematics Teacher 64 (1971), 715--19.
Discusses how the greatest mathematicians have been vitally concerned with the real world. Uses Archimedes, Newton, and Gauss as examples. Archimedes did so much applied work that it is hard to see how he fits Plutarch's description of considering mechanical work ignoble and inferior. The case of Newton is of course well known. An interesting example is Gauss, who used the motto "Thou, nature art my goddess;to thy laws/My services are bound" from Shakespeare's King Lear. Newton and Gauss were also very interested in religion. Philosophy was very important to Gauss. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: Applied Mathematics (General), Archimedes, Isaac Newton (1642-1727), Karl Friedrich Gauss (1777-1855), Religion, and Philosophy. Also possibly relevant: Literature.
Nagy, Dénes. Symmet-origami (symmetry and origami) in art, science, and technology. Symmetry Cult. Sci. 5 (1994), no. 1, 3--12. SC: 00A69 (01A99), MR: 1 309 239.
Discusses the history and philosophy of origami and then (in a little more depth) discusses some of its applications. The author discusses applications in math and science education, and also in art, design, and technology. A particularly interesting application of paper-folding and the theory of polyhedra is in music education, where one researcher devised "a 'tower' of five octahedra, to illustrate some basic concepts in musicology. His inspiration was from a work by Möbius written in 1861. Ganter's compound polyhedron illustrates geometrically the following concepts and their connections: the vertices correspond to the notes of the chromatic scale, the edges corresponds to the thirds and fifths, and the triangular faces correspond to the triads." He mentions that M. C. Escher was interesting in construction paper models (though it is not really clear how deep that interest lay). It is interesting that the well-known book by T. Sundara Row entitled Geometric Exercises in Paper Folding seems to be independent from the Japanese traditions. Closely related topics: Origami, Symmetry, Japan, Education, Music, M. C. Escher, and August Ferdinand Möbius (1790-1868).