Here is a list of our most **popular mathematics proofs**:

#### Algebra (4):

**If a/b=c/d then a/b=(a+c)/(b+d) proof**(blog post)**Completing the square, two geometrical proofs**(blog post)**Derive the quadratic formula from scratch by completing the square**(blog post)**Various ways in which to express the golden ratio**(blog post)

#### Logarithms (1):

**Logarithmic Realms**(PDF file)

**Formulas (5):**

**Deriving the formula for an ellipse from scratch**(blog post)**How to derive the formula for a circle from scratch**(blog post)**Length of an arc formula derived from scratch**(Youtube video)**The Torus formula proof**(zip file)**Mathematical singularity formula proof**(zip file)

#### Visualisation (3):

**Plato’s Meno – Doubling the area of a square**(blog post)**Animation: Doubling the area of a square, Plato’s Meno**(Youtube video)**Understanding proportionality in mathematics**(site page)

#### Areas (8):

**Finding the formulas for areas of triangles**(blog post)**Deriving the formula for the area of an equilateral triangle**(blog post)**Deriving the area of a pentagon**(zip file)**Deriving the area of a circle**(zip file)**Deriving the area of a circle**(Youtube videos)**Deriving the area of a sector using the constant of proportionality**(Youtube video)**Deriving the area of an ellipse**(zip file)**Deriving the area of an ellipse**(Youtube videos)

#### Volumes (2):

**Deriving the volume of a sphere**(zip file)**Deriving the volume of a cone**(zip file)

#### Angles (4):

**Proving that opposite angles are equivalent**(blog post)**Proving that the angles below the apex of an isosceles triangle are equivalent**(blog post)**Thales’ Theorem proof**(blog post)**Finding the angle between two vectors**(blog post)

#### Trigonometry (5):

**Trigonometric identity proofs**(Youtube videos and zip files)**Cosine Rule Mastery**(PDF file)**Sine Rule Mastery**(PDF file)**The quickest Sine Rule proof**(blog post)**sin(0°) to sin(90°), cos(0°) to cos(90°) and tan(0°) to tan(90°) derivations. 15° steps.**(blog post)

**Pythagoras’ Theorem (5):**

**Two ways to derive Pythagoras’ Theorem from scratch**(blog post)**How to come up with Pythagoras’ equation**(Youtube video)**Properties of c squared, Pythagorean Theorem**(blog post)**How to come up with the distance formula – 2 dimensions**(Youtube video)**How to come up with the distance formula – 3 dimensions**(Youtube video)

**Calculus (4):**

**The fundamental theorem of calculus**(blog post)**Trapezium Rule formula derivation**(blog post)**Deriving the Taylor Series from scratch**(blog post)**How to derive Euler’s Identity using the Maclaurin Series**(blog post)

**Vectors (1):**

**Finding the product of two vectors**(blog post)

#### Statistics (1):

#### Irrational Numbers (1):

#### Complex / Imaginary Numbers (1):

**|z_1*z_2|=|z_1|*|z_2|**proof (blog post)

*Page last updated: 25/09/2017 @ 02:05 hrs (UK time). To report a broken link or anything faulty, click here.*