Combinatorics
61 videos • 4,336 views • by Mathematical Visual Proofs
Visual proofs and visualizations connected to combinatorics or combinatorial ideas.
1
All Rectangles in a 5x5 grid (synthwave; enumeration)
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2
Catalan Numbers Enumeration of Lattice Paths and visual Recurrence Formula (synthwave)
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3
Pascal's Triangle from Lattice Paths (synthwave; enumeration; combinatorics)
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4
The Binomial Recurrence from Lattice Paths (visual proof)
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5
Counting Rectangles in a Square Grid (synthwave; enumeration; visual proof)
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6
Young Diagrams of Integer Partitions up to 12 (synthwave; enumeration)
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7
Generalized Petersen Graphs up to n=10 (synthwave; enumeration)
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8
Four Set Venn Diagram and Five Set Venn Diagram [Discrete Math Class; Visual Proof]
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9
Sum and Product Principles for Finite Sets [Discrete Math Class; Visual Proof]
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10
Elementary Counting Principles [Discrete Math Class]
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11
Combinatorial Objects: Permutations and Subsets [Discrete Math Class]
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12
Three Set Inclusion/Exclusion (visual proof) [Discrete Math Class]
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13
Donuts and Dividers - Unordered Selections with Repetition [Discrete Math Class]
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14
Fibonacci domino tilings of (2 x n)-grid (synthwave enumeration)
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15
Describing Sequences [Discrete Math Class]
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16
Pell Number Lattice Path Enumeration and visual recurrence formula (synthwave; visual proof)
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17
Geometric Sequences and their Sums [Discrete Math Class]
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18
Polynomial Fitting for Sequences [Discrete Math Class]
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19
The Base 1.5 Representation Tree (fractional base visual construction)
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20
Recurrence for partitions into k parts (visual proof)
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21
Solving Two Term Linear Homogenous Recurrences [Discrete Math Class]
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22
Six Sierpiński Triangle Constructions (visual mathematics)
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23
Chebyshev Polynomials of the First Kind (synthwave enumeration)
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24
Lucas Number Circular Tilings (synthwave enumeration)
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25
A Dozen Proofs: Sum of Integers Formula (visual proofs) #SoME2
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26
Sum of Cubes IV (Nicomachus's Theorem)
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27
Sum of Triangular Numbers II (visual proof via cannonballs)
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28
A Multiplicative Triangular Number Recurrence (visual proof)
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29
Visual Sum of Squares III (proof without words)
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30
Geometric series: sums of powers of 8 (visual proof)
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31
The Thue-Morse Sequence (with visualizations)
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32
Sums of Oblong Numbers I (visual proof without words)
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33
Adding pentagonal numbers in 3D (proof without words)
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34
A Dramatic Finite Sum : Oblong Numbers II (visual proof without words)
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35
Every Cube is an Arithmetic Sum (visual proof without words)
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36
Unbelievable Equal Consecutive Sums (3D visual proof)
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37
Walking city streets: Catalan Closed Form (visual proof from lattice paths)
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38
Visual Inclusion/Exclusion
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39
Finite Geometric Sum Formula
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40
Summing cubes with lines of squares
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41
Four Set Venn Diagram?
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42
North/East Lattice Paths
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43
Restricted Lattice Path Enumeration #catalan
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44
3D Visual Sum of Odd Squares | proof without words
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45
An Amazing way to Sum Squares (visual proof V using cuboids)
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46
Sum Cubes with Triangles (visual proof without words V)
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47
Geometry of the Twelve Days of X-mas (visual proof)
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48
Sum of Squares Visual Proofs: From Level 1 to Level 5
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49
Best sum of odds proof?
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50
Best sum visual proof?
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51
3D Sum of Triangular Numbers (visual proof without words III)
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52
Sum of Cubes as Sum of Odds and more (visual proof VI)
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53
Fano Plane: The World’s Smallest Projective Geometry
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54
Tri-Nums Sums! (visual proof IV)
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55
Five set Venn diagram
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56
Sum of Odd Cubes is Triangular (visual proof without words)
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57
Infinitely Many Infinite Sums Geometrically (visual proof)
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58
Sum of Cubes VII (visual proof without words)
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59
Two Geometric Series in an Isosceles Trapezoid (visual proof without words)
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60
Dancing tilings - why this pattern?
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61
Can you explain the pattern?
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