# What's missing from Khan Academy?

## Writing single-digit numbers as numerals and words (kindergarten)

Identified by inspection


Kindergarten Math Course
by JoAnn's School

## Congruent complements theorem (description and proof)

Identified by search


What is the Congruent Complements Theorem?
by Wrath of Math

Congruence Complements Theorem
by Math Teacher

## Congruent supplements theorem (description and proof)

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Congruence Supplements Theorem
by Math Teacher

## Proof: The square root of any non-perfect square is irrational

Identified by inspection


Proof that the square root of ANY integer is irrational (besides perfect squares)
by Mu Prime Math

## False proofs

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Proof that 1 = 2.
by John Hush

Proof that 0 = 1
by John Hush

A Proof that 0 = 1 (Can You Spot the Mistake?)
by patrickJMT

## Water jug riddles

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How not to Die Hard with Math
by Mathologer

## Futoshiki puzzles

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Futoshiki (fun puzzle with inequalities)
by Eddie Woo

## Finger multiplication tricks (and their correctness proofs)

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Finger multiplication on steroids
by Mathologer

## Two proofs: Area of dodecagon

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Area of a Regular Dodecagon (visual proof)
by Micro Visual Proofs

Area of a Regular Dodecagon II (visual proof)
by Micro Visual Proofs

## Po-Shen Lo method

Identified by inspection


a new algebra 2 quadratic formula
by Dr Peyam Show

## Proof: Inverse Pythagorean theorem

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Pythagorean Theorem and Its Inverse
by blackpenredpen

## Palindromic polynomials

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Magic Polynomials
by Dr Peyam Show

## Division as repeated subtraction

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and inspection


North School Math - Repeated Sub Strategy
Londonderry, NH North Elementary School

## KenKen puzzles

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Tom Davis, "KenKen"
by Math Circle Network

## River crossing puzzles

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River Crossings
by JRMF

## Patterns in Pascal's triangle

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nCr Notation (2 of 2: The mystery of the prime rows in Pascal's Triangle)
by Eddie Woo

## Viviani's theorem (description and proof)

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First visual proof:

Geometry: Viviani's theorem | Visualization + Proof |
by Think Twice

Second visual proof:

Viviani's theorem
by Wikipedia

## Proof: Exactly 3 regular tessellations

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Geometry 9.6b, Tessellations, Regular, Semi-regular, or neither
by JoAnn's School

## Intro to triangular numbers

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What are Triangular Numbers?
by Learning at Home with Mr B

## Visual proof: Sum of the first n triangular numbers

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Sum of n Triangular Numbers - Animation
by Mathocube

## Ptolemy's theorem

Identified by inspection


Proof:

How to Prove Ptolemy's Theorem for Cyclic Quadrilaterals
by ProfOmarMath

Visual proof:

A Beautiful Proof of Ptolemy's Theorem.
by MathyJaphy

## Fuhrmann's theorem

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fuhrmann's theorem
by Wilson Stother

## British flag theorem

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British Flag Theorem
by AoPS

## 0.999... = 1

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Does 0.99999.. equal one or does it not?
by Mathematical Association of America

## Proof: Converse of the Pythagorean theorem

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Proof of the Converse of Pythagoras' Theorem
by KeysToMaths1

## Circumcenter theorem

This topic occurs in "Geometry (all content)," but belongs in "High school geometry."

Circumcenter of a triangle

## Expanding and factoring with algebra tiles

Identified by search

and inspection


Factoring Simple Trinomials Using Algebra Tiles
by MrsALovesMath

6.5 Factoring Trinomials with Algebra Tiles
by Algebra 1 - Ladue Mathematics

## t-results

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Search "eddie woo t-results" on YouTube.

## Multiplying two binomials using algebra tiles

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Visual Proof for Difference of Squares a²-b² by Eddie Woo

## Adding and subtracting integers using two color counters

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## Proof: Exactly 5 Platonic solids

Identified by search


Mysterium Cosmographicum
by D!NG

## Solving factorial equations

Identified by search


How to solve equations with Factorials
by Anil Kumar

Divisibility rules for 7 and 13
Proving the divisibility rules for 7 and 13
Sum of first n odd numbers?
Most visual proofs
Visual proof: Difference of cubes
Most topics concerning even and odd functions
Sophie Germain's identity
Gauss's trick for tetrahedral numbers
Hard problems
Variations on the Monty Hall problem
Billiard bouncing puzzles?
Golf puzzles?
Area mazes?
Geometry puzzles?
Textbook recommendations
Nim-like games
Math circles