Text 1 

Geometry allows us to explore the properties of space in terms of plan (two-dimensional) figures and solid (three-dimensional) figures. We can use geometric techniques to draw a line of an exact length, bisect a line, bisect an angle, construct a triangle, and calculate the area of a sphere. The principles of geometry were laid down by the Greek mathematician Euclid (C. 330 BC-275 BC) and have remained almost unchanged ever since. Map-making; surveying, designing, architecture, and computer circuitry all depend on geometry in their precise use of angles, figures, and volume.

Text 2 

Triangles, squares, and pentagons are all examples of polygons. A regular polygon has sides of equal length and interior angles of equal size. The more sides a regular polygon has, the more it will resemble a circle. There are two kinds of polygon: the convex and the reentrant. The convex polygon has all of its corners pointing inward. The reentrant polygon has one or more corners pointing inward.

Text 3 

Angles are formed where two straight lines meet. They can be measured using a protractor or an angle indicator. Angles are measured in units called degrees. A degree is obtained by dividing the circumference of a circle into 360 equal-sized parts. Mathematicians use a small circle as a symbol to indicate degrees. The angle that occurs at the corners of squares and other rectangles is 90 degrees and is called a right angle. Angles of less than 90 are called acute angles. Angles measuring between 90 and 180 are called obtuse angles. Angles measuring between 180 and 360 are called reflex angles.

Text 4 

A transformation is a change in the position, size, or shape of a geometric figure (such as a triangle). The main transformations are reflection, enlargement, translation, and rotation. Other forms of transformations include stretching and shearing. Reflection, translation, and rotation change the position of the figure. They do not alter the lengths of the sides or the area of the figure and so are called isometries. Stretching increases the size of the figure along one axis. Shearing is similar to stretching but the area of the figure remains the same. Enlargement increases the size of the whole figure.

Text 5 

Topology is a modern branch of geometry that takes real problems, such as how to plan a freeway intersection, and converts them into spatial puzzles. Spatial puzzles can be used to represent three-dimensional problems in a two-dimensional way. This often makes the problem easier to solve. Topology grew out of attempts to solve the Konigsberg Bridge problem.