A geoboard is a mathematical manipulative used to explore basic concepts in

plane geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...

such as

perimeter A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimet ...

area Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-di ...

and the characteristics of

triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

s and other

polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...

s. It consists of a physical board with a certain number of nails half driven in, around which are wrapped geo bands that are made of rubber. Normal rubber bands can also be used. Geoboards were invented and popularized in the 1950s by Egyptian mathematician Caleb Gattegno (1911-1988).

Structure and use

Geoboard is a board. A variety of boards are used. Originally made out of plywood and brass nails or pegs, geoboards are now usually made out of plastic. They may have an upright

square lattice In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as . It is one of the five types of two-dimensional lattices as classified by their ...

of 9, 16 or 25 nails or more, or a circle of nails around a central nail. Students are asked to place rubber bands around the nails to explore geometric concepts or to solve mathematical puzzles. Geoboards may be used to learn about: