Select your city
Resources
Syllabus
“Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi”
Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.
Albert Einstein was born on March 14, 1879: the birthday of one of the greatest geniuses of all time is the date chosen by many mathematicians to remember and celebrate Greek Pi. The translation of the date also corresponds to the numbers “3, 14”.
More accurately, March 14th, at 1:59:26.5 which is 3.14159265 correct to 8 decimals!!
Pi (often represented by the lower-case Greek letter “π”), one of the most well-known mathematical constants, is the ratio of a circle’s circumference to its diameter. For any circle, the distance around the edge is a little more than three times the distance across. Pi is actually an irrational number (a decimal with no end and no repeating pattern) that is most often approximated with the decimal 3.14 or the fraction 22/7.
Pi occurs in many areas of mathematics, far too many to list here.
The study of pi begins around middle school, when students learn about the circumference and area of circles.
The definition of pi gives us a way to calculate circumference. If π = C/d, then C = πd. The circumference of a circle is also C = 2πr.
The area of a circle is A = πr2.
The surface area of a cylinder is 2πr2 + h(2πr).
The volume of a cylinder is πr2h.
The surface area of a sphere is 4πr2.
The volume of a sphere is (4/3)πr3.
The surface area of a cone is πrl + πr2.
The volume of a cone is (1/3)πr2h.
In high school, students study circles more in-depth and also study unit-circle trigonometry.
Angles can be measured in both degrees and radians. A radian is defined as an arc that has the same measure as the radius of a circle. Since π diameters equal circumference, 2π radius lengths also equals circumference. Therefore, 360 degrees is the same as 2π radians, 180 degrees equals π radians, 90 degrees equals π/2 radians, etc.
An arc created by a central angle, θ, is a fraction of the circumference of a circle: arc length = θ(C/2π). The equation for circumference can be substituted in, then the whole equation can be simplified to: arc length = θ(πd/2π)=θ(d/2)=θr.
The area of a sector created by a central angle θ is a fraction of the area of a circle: area of sector = θ(A/2π). The equation for area can be substituted in, then the whole equation can be simplified to: area of sector = θ(πr2/2π)=θ(r2/2).
