A history of geometry in the world of mathematics

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.

A history of geometry in the world of mathematics

Differential geometry The German mathematician Carl Friedrich Gauss —in connection with practical problems of surveying and geodesy, initiated the field of differential geometry.

Using differential calculushe characterized the intrinsic properties of curves and surfaces. For instance, he showed that the intrinsic curvature of a cylinder is the same as that of a plane, as can be seen by cutting a cylinder along its axis and flattening, but not the same as that of a spherewhich cannot be flattened without distortion.

Instead, they discovered that consistent non-Euclidean geometries exist. Topology Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing.

The continuous development of topology dates fromwhen the Dutch mathematician L. Brouwer — introduced methods generally applicable to the topic.

A history of geometry in the world of mathematics

History of geometry The earliest known unambiguous examples of written records—dating from Egypt and Mesopotamia about bce—demonstrate that ancient peoples had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers.

It concludes with a brief discussion of extensions to non-Euclidean and multidimensional geometries in the modern age. Similarly, eagerness to know the volumes of solid figures derived from the need to evaluate tribute, store oil and grain, and build dams and pyramids.

Even the three abstruse geometrical problems of ancient times—to double a cube, trisect an angle, and square a circle, all of which will be discussed later—probably arose from practical matters, from religious ritual, timekeeping, and construction, respectively, in pre-Greek societies of the Mediterranean.

And the main subject of later Greek geometry, the theory of conic sectionsowed its general importance, and perhaps also its origin, to its application to optics and astronomy.

Mathematics in the 9th century

While many ancient individuals, known and unknown, contributed to the subject, none equaled the impact of Euclid and his Elements of geometry, a book now 2, years old and the object of as much painful and painstaking study as the Bible.

Much less is known about Euclidhowever, than about Moses. Euclid wrote not only on geometry but also on astronomy and optics and perhaps also on mechanics and music. Only the Elements, which was extensively copied and translated, has survived intact.

A history of geometry in the world of mathematics

What is known about Greek geometry before him comes primarily from bits quoted by Plato and Aristotle and by later mathematicians and commentators. Among other precious items they preserved are some results and the general approach of Pythagoras c.

The Pythagoreans convinced themselves that all things are, or owe their relationships to, numbers. The doctrine gave mathematics supreme importance in the investigation and understanding of the world.

Plato developed a similar view, and philosophers influenced by Pythagoras or Plato often wrote ecstatically about geometry as the key to the interpretation of the universe. Thus ancient geometry gained an association with the sublime to complement its earthy origins and its reputation as the exemplar of precise reasoning.

Finding the right angle Ancient builders and surveyors needed to be able to construct right angles in the field on demand. One way that they could have employed a rope to construct right triangles was to mark a looped rope with knots so that, when held at the knots and pulled tight, the rope must form a right triangle.

The simplest way to perform the trick is to take a rope that is 12 units long, make a knot 3 units from one end and another 5 units from the other end, and then knot the ends together to form a loop, as shown in the animation.

However, the Egyptian scribes have not left us instructions about these procedures, much less any hint that they knew how to generalize them to obtain the Pythagorean theorem: The required right angles were made by ropes marked to give the triads 3, 4, 5 and 5, 12, In Babylonian clay tablets c.

A right triangle made at random, however, is very unlikely to have all its sides measurable by the same unit—that is, every side a whole-number multiple of some common unit of measurement.

This fact, which came as a shock when discovered by the Pythagoreans, gave rise to the concept and theory of incommensurability. Locating the inaccessible By ancient tradition, Thales of Miletuswho lived before Pythagoras in the 6th century bce, invented a way to measure inaccessible heights, such as the Egyptian pyramids.

Although none of his writings survives, Thales may well have known about a Babylonian observation that for similar triangles triangles having the same shape but not necessarily the same size the length of each corresponding side is increased or decreased by the same multiple.

A determination of the height of a tower using similar triangles is demonstrated in the figure. A comparison of a Chinese and a Greek geometric theoremThe figure illustrates the equivalence of the Chinese complementary rectangles theorem and the Greek similar triangles theorem.

Estimating the wealth A Babylonian cuneiform tablet written some 3, years ago treats problems about dams, wells, water clocks, and excavations. Ahmesthe scribe who copied and annotated the Rhind papyrus c. Euclid arbitrarily restricted the tools of construction to a straightedge an unmarked ruler and a compass.

The restriction made three problems of particular interest to double a cube, to trisect an arbitrary angle, and to square a circle very difficult—in fact, impossible.

Various methods of construction using other means were devised in the classical period, and efforts, always unsuccessful, using straightedge and compass persisted for the next 2, years.

Doubling the cube The Vedic scriptures made the cube the most advisable form of altar for anyone who wanted to supplicate in the same place twice. The rules of ritual required that the altar for the second plea have the same shape but twice the volume of the first.

The problem came to the Greeks together with its ceremonial content. An oracle disclosed that the citizens of Delos could free themselves of a plague merely by replacing an existing altar by one twice its size.

The Delians applied to Plato. Hippocrates of Chioswho wrote an early Elements about bce, took the first steps in cracking the altar problem.Read on and enjoy learning a brief history of geometry before taking a look at all our other interesting information devoted to the wonderful world of mathematics.

The word ‘geometry’ comes from the Greek words ‘geo’, meaning earth, and ‘metria’, meaning measure. 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). The discipline of mathematics now covers - in addition to the more or less standard fields of number theory, algebra, geometry, analysis (calculus), mathematical logic and set theory, and more applied mathematics such as probability theory and statistics - a bewildering array of specialized areas and fields of study, including group theory.

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.

Mathematics lessons for elementary, middle, and high school including geometry. Cynthia Lanius. Thanks to PBS for permission to use the Pyramid photo.

History of Geometry Egyptians: A search for a better answer to that question has intrigued mathematicians throughout history. Coordinate Geometry. The History of Geometry. Geometry's origins go back to approximately 3, BC in ancient Egypt.

Ancient Egyptians used an early stage of geometry in several ways, including the surveying of land, construction of pyramids, and astronomy.

History of geometry - Wikipedia