The Sierpinski Triangle

In the first episode of Math Proof Monday, The Newton Frontier discusses the Sierpinski triangle, a fractal named after Polish Mathematician Waclaw Sierpinski. We then go on to provide a proof of the area and perimeter of a Sierpinski triangle.

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credit for opening animations goes to MicroChemicals:

[thenewtonfrontier]

A Couple Notes:

I just realized for n = 3, I drew the triangle incorrectly. Please pardon the mistake.

Also, as for the audio levels in the beginning, Premiere Pro screwed a couple things up. I'll look into fixing it.

Thanks,
Tyler

[David-gpfd]

LSD showed me this shape once before ever seeing it. Beautiful

[elotimmi]

The pace is very good, and you don’t skip the steps. Amazing video🫶🫶

[Chickadee]

Hey, great video! I enjoyed the clear and digestible explanations. Keep up the good work!

[FurryAzzre]

The Final Shape,
The Flawless Shape,
Divinity,
Harmony,
Prosperity,
Majesty,
The All-Shape,
The Law of 3,
Knowledge Given Form,
Breath of Formity,
The Trigonometress’s Purity,
The Edge of Unity.

Many names, the Azzeri call this divine shape, but simply refered to as:

The Triagon.

[winstongludovatz]

Huge gaps: exactly what is the limit structure, the area of the finite structures converges to the area of the limit structure. The "perimeter" of the limit structure is undefined. The boundary is defined but why should that be a curve which has a length.