Geometry History

Geometry began with a practical need to measure shapes. The word geometry means to “measure the earth” and is the science of shape and size of things.

Around 2900 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 2000 BC. The Egyptians (5000–500 BC) and the Babylonians (4000–500 BC) developed practical geometry to solve everyday problems.

Geometry in ancient times was recognized as part of everyone's education. Ancient knowledge of the sciences was often wrong and wholly unsatisfactory by modern standards. However not all of the knowledge of the more learned peoples of the past was false. First man created a number system of base 10. When our primitive ancestors first discovered the need to count they definitely would have used their fingers to help them. As an object of a higher thinking, man invented ten number-sounds. The needs and possessions of a primitive man were not many. When the need to count over ten aroused, he simply combined the number-sounds related with his fingers. So, if he wished to define one more than ten, he simply said “one-ten”.

The Babylonians developed a flexible technique for dealing with fractions. The same system for telling time that is used today was also used by the Babylonians. Also, we use base sixty with circles (360 degrees to a circle). The Babylonians used many of the more common cases of the Pythagorean Theorem for right triangles. They also used accurate formulas for solving the areas, volumes and other measurements of the easier geometric shapes as well as trapezoids. The Babylonian value for pi was a very rounded off three. Because of this crude approximation of pi, the Babylonians achieved only rough estimates of the areas of circles and other spherical, geometric objects. The real birth of modern math was in the era of Greece and Rome. The philosophers of Greece used mathematical formulas to prove propositions of mathematical properties.

So, as you might have realized, without the great minds of the past our mathematical experiences would be quite different from the way they are today.

Prisms & Pyramids

A prism is a polyhedron, with two parallel faces called bases. The other faces are always parallelograms. The prism is named by the shape of its base.

A pyramid is a solid object where the base is a polygon (a straight-sided shape) and the sides are triangles which meet at the top (the apex).

Prisms and pyramids are to be treated as classes to group all prisms and all pyramids. Prisms have two bases that are the same shape and size. The bases of a prism may be squares, rectangles, triangles or other polygons. The other faces in the net are rectangular if the faces are perpendicular to the base. The base of a prism is the shape of the uniform cross-section, not necessarily the face on which it is resting.

Pyramids differ from prisms in that they have only one base and all the other faces are triangular. The triangular faces meet at a common vertex.

An important understanding is that the cross-sections parallel to the base of prisms are uniform and the cross-sections parallel to the base of pyramids are not.

In a right prism, the base and top are perpendicular to the other faces. In a right pyramid or cone, the base has a centre of rotation, and the interval joining that centre to the apex is perpendicular to the base (and thus is its axis of rotation).

Oblique prisms, cylinders, pyramids and cones are those that are not right.

Дата добавления: 2015-11-14