Math is Illuminati confirmed (PART 2): Morley's Miracle

TL;DR

Morley's theorem, which states that trisecting the angles of a triangle will result in the formation of an equilateral triangle, is proven using an accessible and beautiful animation-based proof by mathematician John Conway.

Transcript

I'm assuming that you just watched the Illuminati confirmed Video and that you're a hard core mathematician and that you now want the proof that Morley's theorem really works. I'm going to give you a proof now and it's going to be an absolutely amazing proof. Now Morley's theorem is notoriously hard to show. It's very messy, used to be very messy, ... Read More

Key Insights

• 🔺 Morley's theorem states that trisecting the angles of a triangle will result in the formation of an equilateral triangle.
• ❓ John Conway, a mathematician from Princeton University, developed an elegant and accessible proof for Morley's theorem.
• 🔺 The proof involves using the sum of angles in a triangle, the concept of similarity and congruence in triangles, and the idea of equilateral and isosceles triangles.
• 🔺 The proof relies on the fact that the sum of the angles in a triangle is 180 degrees and the ability to scale and superimpose triangles that share angles and segments.
• 🔺 The trisected angles always result in a distribution of angles that are as nice as possible within the triangle.
• 🔺 The proof involves going backwards from the desired equilateral triangle and reconstructing the angles and sides of the trisected triangle.
• 🔺 The proof is supported by the congruence of triangles and the isosceles properties of certain triangles formed in the process.

Questions & Answers

Q: What is Morley's theorem?

Morley's theorem states that if you trisect the angles of a triangle and extend the cuts, the points where the cuts meet will form an equilateral triangle.

Q: How did John Conway contribute to Morley's theorem?

John Conway, a mathematician from Princeton University, developed a beautiful and accessible proof for Morley's theorem.

Q: How does the proof of Morley's theorem involve the sum of angles in a triangle?

One of the key elements in the proof is that the sum of the angles in a triangle is 180 degrees, which helps establish the relationship between the trisected angles.

Q: What is the role of similarity and congruence in the proof of Morley's theorem?

The proof uses the concept of similarity and congruence in triangles to demonstrate the relationships between the angles and sides of the trisected triangles.

Summary & Key Takeaways

• Morley's theorem involves trisecting the angles of a triangle and extending the cuts to find three points that always form an equilateral triangle.

• Mathematician John Conway developed a proof for Morley's theorem that is both elegant and accessible.

• The proof involves using the sum of angles in a triangle, the concept of similarity and congruence in triangles, and the idea of equilateral and isosceles triangles.