## 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, adundant, 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?

If your question has not been answered here please feel free to contact mathschallenge.net by using the email address at the bottom of this page.

Instead you may like to consider the outstanding **Ask Dr. Math ^{®}** (at the Math Forum) which has a large database of FAQ. They also offer a dedicated panel of experts to address individual questions.

http://mathforum.org/dr.math/ (a new window will open)