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Sequencing Props
The converse of III.27--about equal angles and arcs. And sequencing.
Trapped in a Triangle
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.