When was geometry invented

Analytical geometry also referred to as coordinate geometry or cartesian geometry deals with the coordinate system to represent lines and points. In analytical geometry a point is represented by two or three numbers to denote its position on a plane, this is called a coordinate point.

It is written in the form of 3,4 , where 3 is the x-coordinate and 4 is the y-coordinate. We can also have a point 2, 3, 4 where 2 is the x-coordinate, 3 is the y-coordinate and 4 is the z-coordinate. This branch of geometry uses algebraic equations and methods to solve problems.

It also deals with midpoint, parallel and perpendicular lines, line equations, distances between two linear paths. The figure below shows a point 3,4 on a coordinate plane. A branch of geometry that deals with geometric images when they are projected into another surface. It is more inclined towards the point of view of an object. Also, projective geometry does not involve any angle measures. It involves only construction using straight lines and points.

A branch of geometry that deals with curved surfaces and investigating geometrical structures, calculating variations in manifolds, and many more. It uses the concepts of differential calculus. It is mainly used in physics and chemistry for various calculations. Topology is a branch of geometry, which deals with the study of properties of objects that are stretched, resized, and deformed. Topology deals with curves, surfaces, and objects in a three-dimensional surface or a plane.

Check out these interesting articles to know more about the origin of geometry and its related topics. Example 1: Find the area of a circle with radius of 7 units. Example 3: Find the midpoint of a line that passes through 7,3 and 5,1. Geometry is a branch of math that deals with sizes, shapes, points, lines, angles, and the dimensions of two-dimensional and three-dimensional objects.

Coordinate Geometry is a branch of geometry that deals with the position of a point on a plane. Coordinates are denoted as a set of points like 2,3 , which represents the position of a point on a plane. Coordinate geometry uses the concepts of algebra to do calculations for the distance between any two points and to find the angle between two lines and many more. In geometry, an angle is a small figure that is formed at a place where two lines intersect.

Angle is generally measured in degrees. But in math, angles can be measured in both degrees and radians. Pythagoras theorem states, in a right-angled triangle, the sum of the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Piero della Francesca was a highly competent mathematician who wrote treatises on arithmetic and algebra and a classic work on perspective in which he demonstrates the important converse of proposition 21 in Euclid Book VI:b. Piero's converse showed that if a pair of unequal parallel segments are divided into equal parts, the lines joining corresponding points converge to the vanishing point. Piero della Francesca Piero Euclid VI, 21 diagram. This implies that all the converging lines meet at A, the vanishing point at infinity.

Durer "Reclining woman" perspective picture. Albrecht Durer This was a completely new kind of geometry. The fundamental relationships were based on ideas of 'projection and section' which means that any rigid Euclidean shape can be transformed into another 'similar' shape by a perspective transformation. A square can be transformed into a parallelogram think of shadow play and while the number and order of the sides remain the same, their length varies.

In the late 18th century Desargues' work was rediscovered, and developed both theoretically and practically into a coherent system, with central concepts of invariance and duality. In Projective geometry lengths, and ratios of lengths, angles and the shapes of figures, can all change under projection. Parallel lines do not exist because any pair of distinct lines intersect in a point. Another important concept in projective geometry is duality. In the plane, the terms 'point' and 'line' are dual and can be interchanged in any valid statement to yield another valid statement.

In spite of the practical inventions of Spherical Trigonometry by Arab Astronomers, of Perspective Geometry by Renaissance Painters, and Projective Geometry by Desargues and later 18th century mathematicians, Euclidean Geometry was still held to be the true geometry of the real world.

Nevertheless, mathematicians still worried about the validity of the parallel postulate. In the English mathematician John Wallis had translated the work of al-Tusi and followed his line of reasoning. To prove the fifth postulate he assumed that for every figure there is a similar one of arbitrary size.

However, Wallis realized that his proof was based on an assumption equivalent to the parallel postulate. Saccheri's title page. Girolamo Saccheri entered the Jesuit Order in He went to Milan, studied philosophy and theology and mathematics. He became a priest and taught at various Jesuit Colleges, finally teaching philosophy and theology at Pavia, and holding the chair of mathematics there until his death.

Saccheri knew about the work of the Arab mathematicians and followed the reasoning of al-Tusi in his investigation of the parallel postulate, and in he published his famous book, Euclid Freed from Every Flaw. Saccheri assumes that i a straight line divides the plane into two separate regions and ii that straight line can be infinite in extent. These assumptions are incompatible with the obtuse angle case, and so this is rejected. However, they are compatible with the acute angle case, and we can see from his diagram fig.

The irony is that in the next twenty or so pages, in order to show that the acute angle case is impossible, he demonstrates a number of elegant theorems of non-Euclidean geometry! It was clear that Saccheri could not cope with a perfectly logical conclusion that appeared to him to be against common sense. Saccheri's work was virtually unknown until when it was discovered and republished by the Italian mathematician, Eugenio Beltrami As far as we know it had no influence on Lambert, Legendre or Gauss.

Johan Heinrich Lambert Johan Heinrich Lambert followed a similar plan to Saccheri. He investigated the hypothesis of the acute angle without obtaining a contradiction. Lambert noticed the curious fact that, in this new geometry, the angle sum of a triangle increased as the area of the triangle decreased. Many of the consequences of the Parallel Postulate, taken with the other four axioms for plane geometry, can be shown logically to imply the Parallel Postulate.

For example, these statements can also be regarded as equivalent to the Parallel Postulate. Carl Friedrich Gauss Gauss was the first person to truly understand the problem of parallels.

He began work on the fifth postulate by attempting to prove it from the other four. But by he was convinced that the fifth postulate was independent of the other four, and then began to work on a geometry where more than one line can be drawn through a given point parallel to a given line. He told one or two close friends about his work, though he never published it and in a private letter of he wrote:.

The final breakthrough was made quite independently by two men, and it is clear that both Bolyai and Lobachevski were completely unaware of each other's work. Nikolai Ivanovich Lobachevski Nikolai Ivanovich Lobachevski did not try to prove the fifth postulate but worked on a geometry where the fifth postulate does not necessarily hold. Lobachevski thought of Euclidean geometry as a special case of this more general geometry, and so was more open to strange and unusual possibilities.

In he published the first account of his investigations in Russian in a journal of the university of Kazan but it was not noticed. His original work, Geometriya had already been completed in , but not published until Lobachevski explained how his geometry works, "All straight lines which in a plane go out from a point can, with reference to a given straight line in the same plane, be divided into two classes - into cutting and non-cutting.

The boundary lines of the one and the other class of those lines will be called parallel to the given line. Geometry began with a practical need to measure shapes. It is believed that geometry first became important when an Egyptian pharaoh wanted to tax farmers who raised crops along the Nile River. Around BC the first Egyptian pyramid was constructed. Knowledge of geometry was essential for building pyramids, which consisted of a square base and triangular faces.

The earliest record of a formula for calculating the area of a triangle dates back to BC. The Egyptians — BC and the Babylonians — BC developed practical geometry to solve everyday problems, but there is no evidence that they logically deduced geometric facts from basic principles. Thales is credited with bringing the science of geometry from Egypt to Greece.

Thales studied similar triangles and wrote the proof that corresponding sides of similar triangles are in proportion. The next great Greek geometer was Pythagoras — BC. Pythagoras is regarded as the first pure mathematician to logically deduce geometric facts from basic principles. Pythagoras founded a brotherhood called the Pythagoreans, who pursued knowledge in mathematics, science, and philosophy.

Some people regard the Pythagorean School as the birthplace of reason and logical thought. The most famous and useful contribution of the Pythagoreans was the Pythagorean Theorem.