Crank 0 Partitions and the Parity of the Partition Function
[E]
Determine if a formula can be derived to find the number iterations it takes to reach zero or the Kaprekar Constant (6174) without going through the Kaprekar Routine.
[E]
The Random Fibonacci Sequence
[E]
Discover a method to multiply two numbers represented by the same quadratic form.
[E]
Efficient True Random Number Generation
[E]
Examine the correlation between the Fibonacci sequence and the spiral phyllotaxis, or leaf arrangement, of various plants occurring in nature.
[E]
Test three random number generators (functions in Excel, C++, and Java) and evaluated the results using chi-square values from each experiment to determine which program was most likely to generate unbiased random numbers.
[E]
Prove if Benford's Law applies to randomly generated numbers, and not just to numbers occuring from natural data sets.
[E]
Experimental Verification of the Prime Number Theorem
[E]
Build a binary marble adding machine
[E]
What is a prime number?
[P]
[P]
The Efficiency of Prime-Testing Algorithms
[E]
Pascal like Triangle, Sierpinski like Gaskets and Fibonacci like Sequences.
[P]
A Mathematical Proof of a Relationship between Fibonacci and Lucas Numbers
[E]
Pseudo-Random Numbers
[E]
How to find perfect numbers.
[E]
Is there a general divisibility rule, or pattern, that applies to any number?
[E]
Observe the occurrences of Fibonacci numbers, sequences, the Fibonacci ratio, and the Fibonacci spiral in nature.
[E]
Develope a circle map that represents the Collatz transformation and investigates its properties to make progress in proving the Collatz conjecture.
[E]
Find out if there is a number that will disprove Goldbachs Conjecture
[E]
What patterns are formed when number sequences are translated into different base systems and interpreted in base-10?
[E]
Inverse Symmetry Pattern in the Multiplication Table
[E]
Pi Science Fair Projects