The circumference and Area of a circle

What is the formula relating the circumference to the diameter? centre Diameter Radius

This means APPROXIMATELY EQUAL TO C = ? x d People knew that the circumference is about 3 times the diameter but they wanted to find out exactly. C ≈ 3 x d This means APPROXIMATELY EQUAL TO

The mystery ratio 3.14 is very good and close to the true value What value did you find for the ratio? 3.1-3.2 is pretty good 3.14 is very good and close to the true value For most circumstances we say Circumference ≈ 3.14 x diameter What is the true value of this mystery ratio?????

Archimedes, said C ≈3.1419 x d Early Attempts Egyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x d Archimedes, said C ≈3.1419 x d Fibonacci. In 1220 A.D. said C≈3.1418xd What is the value of the number that multiplies the diameter to give the circumference????

What about the AREA of a circle? First consider a square The area of this square in terms of r is A= 2r x2r = 4r2 r 2r

What about the AREA of a circle? Now consider a circle inside the square The area of the circle must be less than the are of the square A < 4r2 2r r 2r Area = ? xr2

Finding a formulae for the area of a circle

C= πd or C=2πr Semi-circle=πr πr r

Area of Rectangle= Base x Height Area = πr x r Area =πr2

The Area and Perimeter of a Circle A circle is defined by its diameter or radius radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it Diameter The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula A=πr2

The Area and Perimeter of a Circle A circle is defined by its diameter or radius radius The perimeter or circumference of a circle is the distance around the outside The area of a circle is the space inside it Diameter The ratio of π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula C=πr2