The Number Pi
The ratio of circumference to diameter, ≈ 3.14159.
Key idea
The ratio of circumference to diameter, ≈ 3.14159.
In depth
π ≈ 3.14159 is the ratio of circumference to diameter for every circle. It is irrational and transcendental, so its digits never repeat. Ancient mathematicians approximated it with polygons.
Worked example
22/7 ≈ 3.1429 and 355/113 ≈ 3.1415929 are good fraction approximations.
Formula
Real-world uses
- Calculating the length of circular fencing and the volume of cylindrical tanks
Common mistake
Treating π as exactly 3.14 or 22/7 in exact work. Keep π as a symbol until the end.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is The Number Pi?
The ratio of circumference to diameter, ≈ 3.14159. It is a topic at the intermediate level in Geometry.
What is the formula for The Number Pi?
The key formula is π = C/d.
Where is The Number Pi used in real life?
Real-world examples: Calculating the length of circular fencing and the volume of cylindrical tanks.
What should I learn before The Number Pi?
Make sure you are comfortable with Area of a Circle, the previous topic in Geometry.
What is a common mistake with The Number Pi?
Treating π as exactly 3.14 or 22/7 in exact work. Keep π as a symbol until the end.
How can I practise The Number Pi?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after The Number Pi?
Move on to Arc Length of a Circle next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.