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Intro
First considerations
Binomial coefficients
Posing the problem
Constructing examples
What about 5?
What Lies Above Pascal's Triangle?
Extending further upwards
Calculations
Derivative
Intuition
Writing cas as a single function
3 points on vertices
Refined intuition
Proof using calculus
Solving
Conclusion
Idea for the proof
How Many Points Uniquely Define a Triangle?
2 points on vertices
Application
Derivation 1
Explanation
What are Triangular Roots?
My New Favourite Trig Function
Final part of the proof
Proof
1 point on vertices
The floor function
y = ]
Binomial theorem
Constructing an example
Proving continuity
Further examples
Infinitely Nested Integral Problem
A Very Special Data Set
This Equation Describes all Circles in ℝ²
Divisibility by 2
Geometric interpretation
Factorisation
Derivation 2
Problems with the original formula
Problems with the new formula
Working modulo 5
Proving the pattern continues
Formal definition
Using the approximation
A Fun Number Theory Problem
Another Ridiculous Approximation?
Setup with complex numbers
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