T H E W A R P I N G T E S S E R A C T
T E S S E R A C T

# Triangle Calculator

YIKES!
Nasty error message here.
Provide sufficient information to determine a triangle, and we'll calculate the rest.
Still a work in progress. Certain combinations of inputs may not be recognized despite uniquely identifying a triangle.

# Single Digit Representation of a Number

Given a number N and a digit D, can you find an expression that contains only D and the operators +, -, *, / and concatenation

Concatenation (+) is the operation of joining two numbers or strings end-to-end. For example, the concatenation of '4' and '9' is '49'.

and evaluates to N? We sure can (most of the time).
Performable operations:

# Chinese Remainder Theorem

In number theory, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.

# Prime Number Calculator

Enter any number, and we will give you all the primes less than or equal to it.
Computation time increases exponentially with greater inputs.

# GoldBach Conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even whole number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort.

# Kaprekar's Constant

Type in any 3 or 4 digit number which isn't a monodigit (something that's not like 1111 or 222).
If the difference between the descending and ascending orders of the number results in a monodigit, the number won't work either.
The difference between the descending and ascending orders of the number will eventually reach 6174 in case of 4 digits or 495 in case of 3 digits, aka Kaprekar's Constant.

# Collatz Conjecture

The Collatz conjecture is a conjecture in mathematics that concerns the following sequence.
Enter any positive integer n. Then, if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always end at 1. Try it out!
'' signifies the operation ((n × 3) + 1)
'' signifies the operation (n ÷ 2)