## Frequently Asked Questions

This section has been produced in response to the continued FAQ received, often relating to one of the published solutions or just general curiosity.

**Number**

- Prime Numbers What is a prime number?
- Number of Primes How many primes are there?
- Number of Divisors How many divisors does a number have?
- Sum of Divisors How do you work out the sum of divisors?
- Perfect Numbers What are perfect, abundant, and deficient numbers?
- Irrational Roots When is a square root irrational?
- Figurate/Polygonal Numbers What are square and triangle numbers?
- Sum of Squares How do you find the sum of square numbers?
- Sum of Cubes Is there a formula to add a sequence of cubes?
- Fibonacci Numbers What are Fibonacci numbers?
- 0.999... Is 0.999... really equal to 1?
- Division by Zero Why are you not allowed to divide by zero?
- Number System What are rational, irrational, real, imaginary, complex, algebraic, and transcendental numbers?
- Roman Numerals How do you read and write Roman numerals?

**Geometry**

- Angle Properties What are the fundamental angle properties?
- Circle Theorems How do you prove the circle theorems?
- Trigonometry What is trigonometry?
- Pythagorean Theorem How do you prove the Pythagorean Theorem?
- Trigonometric Ratios/Identities Where do sin, cos, tan, sec, cosec, and cot comes from?
- General Trigonometry How do you work out lengths/angles in a general triangle?
- Area of Planar Shapes How do you find the area of planar shapes?
- Circumference of a Circle How do you find the circumference of a circle?
- Area of a Circle How do you find the area of a circle?
- Volume of a Prism How do you find volume of a prism?
- Volume of a Pyramid How do you find volume of a pyramid?
- Volume of a Sphere How do you find volume of a sphere?
- Surface Area of a Sphere How do you find surface area of a sphere?

**Constructions**

- Basic Constructions What are the principles of basic constructions?
- Polygonal Constructions How do you construct basic polygons?
- Geometrical Arithmetic Can you do basic arithmetic geometrically?
- Geometrical Square Root How do you perform a square root geometrically?
- Geometrical Quadratic Is it possible to solve quadratics geometrically?
- Impossible Constructions Are any constructions impossible?
- Trisecting an Angle Is it impossible to trisect an angle?
- Constructing a Heptagon Is it impossible to construct a heptagon?

**Code Breaking**

- Cryptography What is cryptography?
- Monoalphabetic Substitution How does basic substitution work?
- Polyalphabetic Substitution Can you make the basic substitution method more secure?
- Transposition What is a shuffle/transposition cipher?
- Frequency Lists Are there useful strategies in decryption?
- Binary and Hexadecimal What are binary and hexadecimal codes?
- ASCII Codes What is ASCII?