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Sequencing Props

The converse of III.27--about equal angles and arcs. And sequencing.

Trapped in a Triangle

Learn some programming. It'll help you learn math.

Turning the Dials

Boring proof of III.27. Also, I F*cking Love Math.

Perps and Diagonals

The sum of perpendiculars to diagonals in a rectangle.

Stirring Up a Proof

A proof requiring just memory and practice.

Touching Circles

A seemingly obvious Proposition III.12 from the Elements.

Proposition II.4

Animated setup for II.4. Then it peters out.

The Distributive Property

Some interactive work with II.1, a geometric Distributive Property.

Extending Pythagoras

Pappus' extension of I.47, the Pythagorean Theorem. And blobs.

Combining Theorems

Three proofs in one (I.34, I.37, and I.41). And a simulation.

Angles in a Triangle

Euclid's proof (I.32) that a triangle's angle measures have a sum of 180\(^\circ\).

Elegance Schmelegance

Proof of a 2005 Math Olympiad problem.

\(\small\Delta\) Midsegment Theorem

Proof using SAS and congruent corresponding angles.

Varignon's Theorem

Interactive demo and proof using Midsegment Theorem.

Fibonacci Sequence

A musical pattern in the Fibonacci numbers.

Spacetime

Spacetime graphs and some basic ideas in special relativity.

Alternate Interior \(\small\measuredangle\)s

Euclid's proof of I.27 and some discussion about 'transitional' topics in math.

Secant Theorem

Proof using inscribed angles and AA similarity.

Formula for Intensity

The formula is related to simple division and graphed.

Side-Angle-Side

Euclid's proof of I.4 and some discussion about precision.

Inscribed \(\small\measuredangle\) Theorem

Proof involves 3 cases. Uses the base angle and exterior angle theorems.

Pick's Theorem

Interactive demo and proof. Some notes about speculation in math.

Vertical \(\small\measuredangle\) Theorem

Proof of I.15 using I.13. Explains where vertical angles got their name.

\(\small\Delta\) Inequality Theorem

Proof and discussion about intuition in mathematics.

The Cissoid

Demo and explanation of the cissoid curve. Other stuff too.

Angle-Side-Angle

Proof by contradiction of I.26. Some notes about how it was first used.

Ceva's Theorem

Interactive proportionality demo. Then the proof.