Geometry
Geometry (from Ancient Greek: Γεωμετρία (romanized: Geometria (English: "Land measurement") derived from Γη (romanized: Ge; English: "Earth" or "land") and also derived from Μέτρον) (romanized: Métron; English: "A measure")) is a branch of mathematics that studies the size, shapes, positions and dimensions of things. We can only see shapes that are flat (2D) or solid (3D), but mathematicians (people who study math) are able to study shapes that are 4D, 5D, 6D, and so on.
Squares, circles and triangles are some of the simplest shapes in flat geometry. Cubes, cylinders, cones and spheres are simple shapes in solid geometry.
Uses
Plane geometry can be used to measure the area and perimeter of a flat shape. Solid geometry can measure a solid shape's volume and surface area.
Geometry can be used to calculate the size and shape of many things. For example, geometry can help people find:
Origins
Geometry is one of the oldest branches of mathematics. Geometry began as the art of surveying of land so that it could be shared fairly between people. The word "geometry" is from a Greek word that means "to measure the land". It has grown from this to become one of the most important parts of mathematics. The Greek mathematician Euclid wrote the first book about geometry, a book called The Elements.
Non-Euclidean geometry
Plane and solid geometry, as described by Euclid in his textbook Elements, is called "Euclidean Geometry". This was simply called "geometry" for centuries. In the 19th century, mathematicians created several new kinds of geometry that changed the rules of Euclidean geometry. These and earlier kinds were called "non-Euclidean" (not created by Euclid). For example, hyperbolic geometry and elliptic geometry come from changing Euclid's parallel postulate.
Non-Euclidean geometry is more complicated than Euclidean geometry but has many uses. Spherical geometry for example is used in astronomy and cartography.
Examples
Geometry starts with a few simple ideas that are thought to be true, called axioms. Such as:
- A point is shown on paper by touching it with a pencil or pen, without making any sideways movement. We know where the point is, but it has no size.
- A straight line is the shortest distance between two points. For example, Sophie pulls a piece of string from one point to another point. A straight line between the two points will follow the path of the tight string.
- A plane is a flat surface that does not stop in any direction. For example, imagine a wall that extends in all directions infinitely.
Geometry Media
The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
Woman teaching geometry. Illustration at the beginning of a medieval translation of Euclid's Elements, (c. 1310).
An illustration of Euclid's parallel postulate
In Euclidean space, a ball is the volume bounded by a sphere
Visual checking of the Pythagorean theorem for the (3, 4, 5) triangle as in the Zhoubi Suanjing 500–200 BC. The Pythagorean theorem is a consequence of the Euclidean metric.
The Koch snowflake, with fractal dimension=log4/log3 and topological dimension=1
A tiling of the hyperbolic plane