Mathematical Exploration

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List of 200 ideas/topics for a Mathematical Exploration
The topics listed here range from fairly broad to quite narrow in scope. It is possible that some of these 200 could be the title or focus of a Mathematical Exploration, while others will require you to investigate further to identify a narrower focus to explore. Do not restrict yourself only to the topics listed below. This list is only the ‘tip of the iceberg’ with regard to potential topics for your Mathematical Exploration. Reading through this list may stimulate you to think of some other topic in which you would be interested in exploring. Many of the items listed below may be unfamiliar to you. A quick search on the internet should give you a better idea what each is about and help you determine if you’re interested enough to investigate further – and see if it might be a suitable topic for your Mathematical Exploration. Algebra and number theory

Goldbach’s conjecture

Probabilistic number theory

Diophantine equations

Continued fractions

Applications of logarithms

Polar equations

Finding prime numbers

Random numbers

Mersenne primes

Magic squares and cubes

Matrices and Cramer’s rule

Divisibility tests

Complex numbers and transformations

Euler’s identity: eiπ + 1 = 0

Fermat’s last theorem
Natural logarithms of complex numbers

Hypercomplex numbers

Diophantine application: Cole numbers

Euclidean algorithm for GCF

Palindrome numbers

Algebraic congruences
Inequalities related to Fibonacci numbers

Boolean algebra

Graphical representation of roots of complex numbers

Fermat’s little theorem

Prime number sieves

Recurrence expressions for phi (golden ratio)


Cavalieri’s principle

Packing 2D and 3D shapes


Heron’s formula

Proofs of Pythagorean theorem

Minimal surfaces and soap bubbles

Map projections

Tiling the plane – tessellations

Morley’s theorem...
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