Geometry also has applications in areas of mathematics that are apparently unrelated. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. A mathematician who works in the field of geometry is called a geometer. Geometry is, along with arithmetic, one of the oldest branches of mathematics. Thales theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle. Since AC is the diameter, the measure of the intercepted arc is 180 degrees-or half the total of 360 degrees in a circle.Geometry (from Ancient Greek γεωμετρία ( geōmetría) 'land measurement' from γῆ ( gê) 'earth, land', and μέτρον ( métron) 'a measure') is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. He was a mentor of famed Greek mathematician Pythagoras, who developed many theorems in mathematics, including several noted in this article.) (This is called Thales theorem, which is named after an ancient Greek philosopher, Thales of Miletus. Mathbits gives this example for finding an inscribed angle:Īn angle inscribed in a semicircle is a right angle. The intercepted arc is the distance of the curve formed between the two points where the chords hit the circle. The formula for finding the inscribed angle is: So, if you have a radius of 4.5 inches:Īn inscribed angle is an angle formed by two chords in a circle which have a common endpoint. You can also calculate the area if a circle if you know the radius. So, if your diameter is 8.5 centimeters, as in the example in the previous slide, you would have:Ī = π(1/2 d)^2 (Area equals pi times one-half the diameter squared.) In this formula, 'A' stands for the area, 'd' represents the diameter, π is pi, or 3.14. The '*' is the symbol used for times or multiplication. In this formula, 'A' stands for the area, 'r' represents the radius, π is pi, or 3.14. The formulas for the area of a circle are:

Think of the area of the circle as if you draw the circumference and fill in the area within the circle with paint or crayons. The area of a circle is the total area that is bounded by the circumference. Or, if you want to know the circumference of a pot that has a radius of 4.5 inches, you would have:Ĭ = 2πr C = 2 * 3.14 * (4.5 in) C = 28.26 inches, which rounds to 28 inches So if you measure the diameter of a circle to be 8.5 cm, you would have:Ĭ = πd C = 3.14 * (8.5 cm) C = 26.69 cm, which you should round up to 26.7 cm Where d is the diameter of the circle, r is its radius, and π is pi. You can calculate the circumference of any circle if you know either the radius or diameter. Pi is the fixed ratio used to calculate the circumference of the circle Pi, which is usually denoted with the Greek letter π, is the ratio of the circle's circumference to its diameter, or approximately 3.14. To measure the circumference of a circle, you need to use 'Pi,' a mathematical constant discovered by the Greek mathematician Archimedes. The '°' is the mathematical symbol for degrees. The circumference of a circle is the measured total length around a circle, which when measured in degrees is equal to 360°. It is denoted by C in math formulas and has units of distance, such as millimeters, centimeters, meters, or inches. The circumference of a circle is its perimeter or distance around it.

Geometric circle