# What's missing from Khan Academy?

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

Identified by inspection https://www.khanacademy.org/math/cc-kindergarten-math

Kindergarten Math Course

by JoAnn's School

## Congruent complements theorem (description and proof)

Identified by search congruent complements site:https://www.khanacademy.org/math/geometry

What is the Congruent Complements Theorem?

by Wrath of Math

Congruence Complements Theorem

by Math Teacher

## Congruent supplements theorem (description and proof)

Identified by search congruent supplements site:https://www.khanacademy.org/math/geometry

Congruence Supplements Theorem

by Math Teacher

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

Identified by inspection https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers#x2f8bb11595b61c86:proofs-concerning-irrational-numbers

Proof that the square root of ANY integer is irrational (besides perfect squares)

by Mu Prime Math

## False proofs

Identified by search false proof site:https://www.khanacademy.org/math/ fallacious proof site:https://www.khanacademy.org/math/ find mistake site:https://www.khanacademy.org/math/

Proof that 1 = 2.

by John Hush

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

by patrickJMT

## Water jug riddles

Identified by search water site:https://www.khanacademy.org/math

How not to Die Hard with Math

by Mathologer

## Futoshiki puzzles

Identified by search futoshiki site:https://www.khanacademy.org/mathFutoshiki (fun puzzle with inequalities)

by Eddie Woo

## Finger multiplication tricks (and their correctness proofs)

Identified by search finger multiply site:https://www.khanacademy.org/math finger multiplication site:https://www.khanacademy.org/math finger product site:https://www.khanacademy.org/mathFinger multiplication on steroids

by Mathologer

## Two proofs: Area of dodecagon

Identified by search dodecagon site:https://www.khanacademy.org/math

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 https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations

a new algebra 2 quadratic formula

by Dr Peyam Show

## Proof: Inverse Pythagorean theorem

Identified by search inverse pythagorean site:https://www.khanacademy.org/math

Pythagorean Theorem and Its Inverse

by blackpenredpen

## Palindromic polynomials

Identified by search palindrome site:https://www.khanacademy.org/math palindromic site:https://www.khanacademy.org/math

Magic Polynomials

by Dr Peyam Show

## Division as repeated subtraction

Identified by search division repeated subtraction site:https://www.khanacademy.org/math/ divide subtract site:https://www.khanacademy.org/math/ and inspection https://www.khanacademy.org/math/arithmetic-home/multiply-divide#division-intro

North School Math - Repeated Sub Strategy

Londonderry, NH North Elementary School

## KenKen puzzles

Identified by search kenken site:https://www.khanacademy.org/math

Tom Davis, "KenKen"

by Math Circle Network

## River crossing puzzles

Identified by search river site:https://www.khanacademy.org/math

## Patterns in Pascal's triangle

Identified by search pascal's triangle site:https://www.khanacademy.org/math

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

by Eddie Woo

## Viviani's theorem (description and proof)

Identified by search viviani site:https://www.khanacademy.org/math viviani's site:https://www.khanacademy.org/math

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

Identified by inspection tessellation site:https://www.khanacademy.org/math tiling site:https://www.khanacademy.org/math

Geometry 9.6b, Tessellations, Regular, Semi-regular, or neither

by JoAnn's School

## Intro to triangular numbers

Identified by search triangular numbers site:https://www.khanacademy.org/math

What are Triangular Numbers?

by Learning at Home with Mr B

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

Identified by search triangular numbers site:https://www.khanacademy.org/math

Sum of n Triangular Numbers - Animation

by Mathocube

## Ptolemy's theorem

Identified by inspection https://www.khanacademy.org/math/engageny-geo/geo-5/geo-5e/a/geo-5e

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

Identified by search fuhrmann site:https://www.khanacademy.org/math

fuhrmann's theorem

by Wilson Stother

## British flag theorem

Identified by search british flag site:https://www.khanacademy.org/math

## 0.999... = 1

Identified by search 0.999 site:https://www.khanacademy.org/math

Does 0.99999.. equal one or does it not?

by Mathematical Association of America

## Proof: Converse of the Pythagorean theorem

Identified by search converse pythagorean site:https://www.khanacademy.org/math

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

by Khan Academy

## Expanding and factoring with algebra tiles

Identified by search algebra tiles site:https://www.khanacademy.org and inspection https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring

Factoring Simple Trinomials Using Algebra Tiles

by MrsALovesMath

6.5 Factoring Trinomials with Algebra Tiles

by Algebra 1 - Ladue Mathematics

## t-results

Identified by search t-results site:https://www.khanacademy.org/math

Search "eddie woo t-results" on YouTube.

## Multiplying two binomials using algebra tiles

Identified by inspection https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring#x2f8bb11595b61c86:multiply-binomial https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring#x2f8bb11595b61c86:special-product-binomials

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

## Adding and subtracting integers using two color counters

Identified by search integers counters site:https://www.khanacademy.org/math

Search "mathispower4u add subtract integers counters" on YouTube.

## Children's book recommendations

## Proof: Exactly 5 Platonic solids

Identified by search platonic site:https://www.khanacademy.org/math

Mysterium Cosmographicum

by D!NG

## Solving factorial equations

Identified by search factorial equation site:https://www.khanacademy.org/math

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? Crossed ladders theorem 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 St. Petersburg paradox? Boy-girl paradox? Converse of each corresponding angle theorem Converse of the Pythagorean theorem Triangle midsegment theorem Solving nested absolute value equations? Finding all the factors of a number using Cuisenaire rods Finding the GCD or LCM of two or more numbers, using Cuisenaire rods