FAQ: Where Did Spherical Geometry Come From?

Greek mathematics … geometry of the sphere (called spherics) were compiled into textbooks, such as the one by Theodosius (3rd or 2nd century bce) that consolidated the earlier work by Euclid and the work of Autolycus of Pitane (flourished c. 300 bce) on spherical astronomy.

Why does spherical geometry exist?

Spherical geometry is important in navigation, because the shortest distance between two points on a sphere is the path along a great circle. Riemannian Postulate: Given a line and a point not on the line, every line passing though the point intersects the line. (There are no parallel lines).

Where did spherical trigonometry originate from?

Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam.

Is spherical geometry the same as elliptical geometry?

Elliptic geometry is an example of a geometry in which Euclid’s parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two).

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What type of geometry is a sphere?

The sphere has for the most part been studied as a part of 3-dimensional Euclidean geometry (often called solid geometry), the surface thought of as placed inside an ambient 3-d space.

Who invented spherical geometry?

geometry of the sphere (called spherics) were compiled into textbooks, such as the one by Theodosius (3rd or 2nd century bce) that consolidated the earlier work by Euclid and the work of Autolycus of Pitane (flourished c. 300 bce) on spherical astronomy.

How is spherical geometry used in real life?

Spherical geometry is useful for accurate calculations of angle measure, area, and distance on Earth; the study of astronomy, cosmology, and navigation; and applications of stereographic projection throughout complex analysis, linear algebra, and arithmetic geometry.

Did aryabhatta invented trigonometry?

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

Who is called Father of trigonometry?

The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. This makes Hipparchus the founder of trigonometry.

Are there parallel lines in spherical geometry?

If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. There are no parallel lines in spherical geometry.

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Who discovered hyperbolic geometry?

The first published works expounding the existence of hyperbolic and other non-Euclidean geometries are those of a Russian mathematician, Nikolay Ivanovich Lobachevsky, who wrote on the subject in 1829, and, independently, the Hungarian mathematicians Farkas and János Bolyai, father and son, in 1831.

What is the difference between Euclidean and spherical geometry?

Euclidean Geometry uses a plane to plot points and lines, whereas Spherical Geometry uses spheres to plot points and great circles. In spherical geometry angles are defined between great circles. The sum of the interior angles of a triangle ALWAYS exceeds 180 degrees.

Why are there no parallel lines in spherical geometry?

In spherical geometry Parallel lines DO NOT EXIST. In Euclidean geometry a postulate exists stating that through a point, there exists only 1 parallel to a given line. Therefore, Parallel lines do not exist since any great circle (line) through a point must intersect our original great circle.

What is spherical shape?

Something spherical is like a sphere in being round, or more or less round, in three dimensions. Apples and oranges are both spherical, for example, even though they’re never perfectly round. A spheroid has a roughly spherical shape; so an asteroid, for instance, is often spheroidal—fairly round, but lumpy.

Is spherical geometry non-Euclidean?

Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The two most common non-Euclidean geometries are spherical geometry and hyperbolic geometry. In spherical geometry there are no such lines.

How was non-Euclidean geometry discovered?

Gauss invented the term “Non-Euclidean Geometry” but never published anything on the subject. On the other hand, he introduced the idea of surface curvature on the basis of which Riemann later developed Differential Geometry that served as a foundation for Einstein’s General Theory of Relativity.

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