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Top Tracks
1
Intro
2
First considerations
3
Binomial coefficients
4
Posing the problem
5
Constructing examples
6
What about 5?
7
What Lies Above Pascal's Triangle?
8
Extending further upwards
9
Calculations
10
Derivative
11
Intuition
12
Writing cas as a single function
13
3 points on vertices
14
Refined intuition
15
Proof using calculus
16
Solving
17
Conclusion
18
Idea for the proof
19
How Many Points Uniquely Define a Triangle?
20
2 points on vertices
21
Application
22
Derivation 1
23
Explanation
24
What are Triangular Roots?
25
My New Favourite Trig Function
26
Final part of the proof
27
Proof
28
1 point on vertices
29
The floor function
30
y = ]
31
Binomial theorem
32
Constructing an example
33
Proving continuity
34
Further examples
35
Infinitely Nested Integral Problem
36
A Very Special Data Set
37
This Equation Describes all Circles in ℝ²
38
Divisibility by 2
39
Geometric interpretation
40
Factorisation
41
Derivation 2
42
Problems with the original formula
43
Problems with the new formula
44
Working modulo 5
45
Proving the pattern continues
46
Formal definition
47
Using the approximation
48
A Fun Number Theory Problem
49
Another Ridiculous Approximation?
50
Setup with complex numbers
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