# A history of geometry in the world of mathematics

Historically, it was regarded as the science of quantity, whether of magnitudes as in geometry or of numbers as in arithmetic or of the generalization of these two fields as in algebra. Some have seen it in terms as simple as a search for patterns.

Their names—located on the map under their cities of birth—can be clicked to access their biographies. Also important were developments in India in the first few centuries ad. Although the decimal system for whole numbers was apparently not known to the Indian astronomer Aryabhata bornit was used by his pupil Bhaskara I inand by the system had reached northern Mesopotamia, where the Nestorian bishop Severus Sebokht praised its Hindu inventors as discoverers of things more ingenious than those of the Greeks.

See South Asian mathematics. Most of the translations were done from Greek and Syriac by Christian scholars, but the impetus and support for this activity came from Muslim patrons. The investigation of such numbers formed a continuing tradition in Islam. Working in the House of Wisdom, he introduced Indian material in his astronomical works and also wrote an early book explaining Hindu arithmetic, the Book of Addition and Subtraction According to the Hindu Calculation.

In another work, the Book of Restoring and Balancinghe provided a systematic introduction to algebraincluding a theory of quadratic equations. Both works had important consequences for Islamic mathematics. This tradition of service to the Islamic faith was an enduring feature of mathematical work in Islam and one that, in the eyes of many, justified the study of secular learning.

Mathematics in the 10th century Islamic scientists in the 10th century were involved in three major mathematical projects: The first of these projects led to the appearance of three complete numeration systems, one of which was the finger arithmetic used by the scribes and treasury officials.

This ancient arithmetic system, which became known throughout the East and Europe, employed mental arithmetic and a system of storing intermediate results on the fingers as an aid to memory.

Its use of unit fractions recalls the Egyptian system. A second common system was the base numeration inherited from the Babylonians via the Greeks and known as the arithmetic of the astronomers.

Although astronomers used this system for their tables, they usually converted numbers to the decimal system for complicated calculations and then converted the answer back to sexagesimals.

The third system was Indian arithmetic, whose basic numeral forms, complete with the zero, eastern Islam took over from the Hindus. Different forms of the numerals, whose origins are not entirely clear, were used in western Islam.

Also, the arithmetic algorithms were completed in two ways: Several algebraists explicitly stressed the analogy between the rules for working with powers of the unknown in algebra and those for working with powers of 10 in arithmetic, and there was interaction between the development of arithmetic and algebra from the 10th to the 12th century.

Although none of this employed symbolic algebra, algebraic symbolism was in use by the 14th century in the western part of the Islamic world. Other parts of algebra developed as well. However, not only arithmetic and algebra but geometry too underwent extensive development.

Ibn al-Haytham, for example, used this method to find the point on a convex spherical mirror at which a given object is seen by a given observer. Not only did he discover a general method of extracting roots of arbitrary high degree, but his Algebra contains the first complete treatment of the solution of cubic equations.

Omar did this by means of conic sections, but he declared his hope that his successors would succeed where he had failed in finding an algebraic formula for the roots.

To this tradition Omar contributed the idea of a quadrilateral with two congruent sides perpendicular to the baseas shown in the figure. The parallel postulate would be proved, Omar recognized, if he could show that the remaining two angles were right angles.

In this he failed, but his question about the quadrilateral became the standard way of discussing the parallel postulate. Quadrilateral of Omar KhayyamOmar Khayyam constructed the quadrilateral shown in the figure in an effort to prove that Euclid's fifth postulate, concerning parallel lines, is superfluous.A Brief History of Greek Geometry.

The Babylonians had an algebraic influence on Greek mathematics. Egyptian geometry was not a science in the way the Greeks viewed geometry.

It was more of a grab bag for rules for calculation without any motivation or . A History of Mathematics (Second edition, revised by Uta C. Merzbach ed.).

New York: Wiley. Jay Kappraff, A Participatory Approach to Modern Geometry, , World Scientific Publishing. Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19 th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a Reviews: 3.

Geometry: Geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

It is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in.

Applied mathematics, which gives us the tools we need to shape the world around us. From the simple arithmetic of counting your change at the store, to the complex functions and equations used to design jet turbines, this field is the practical, hands on side of math.

Show your students that numbers don't have to be difficultin fact, they can be enjoyable! More than just another textbook, this supplement to your curriculum traces the history of mathematics principles and theory; features simple algebra, geometry, and scientific computations; and offers practical tips for everyday math use.

Includes biblical 5/5(4).

Ancient Mathematics - History of Mathematics