Heron's Formula - What Is the Hidden Meaning of 1 + 2 + 3 = 1 x 2 x 3?

Explore the fascinating world of Heron's formula and its extensions in this 27-minute video. Delve into the hidden meaning behind the curious identity 1+2+3=1x2x3, and discover how it relates to Heron's famous formula for calculating triangle areas. Learn about Brahmagupta's and Bretschneider's extensions of this formula, and follow along as the video presents proofs and explanations using trigonometry and geometric animations. Gain insights into the work of mathematicians like Albrecht Hess and explore related concepts such as the Cut-the-knot website and Pythagoras' theorem. Engage with a comprehensive exploration of geometric formulas and their applications in this informative mathematical journey.

Syllabus

Intro.
1+2+3=1x2x3 in action.
Equilateral triangle.
Golden triangle.
Chapter 1: Heron.
Heron's formula.
Brahmagupta's formula.
Bretschneider's formula.
Chapter 2: How? The proof.
Heron via trig .
Cut-the-knot.
Albrecht Hess.
Heron to Brahmagupta proof animation.
Thank you!.
"Maybe one of you can check in the comments" is the new "left as an exercise to the reader" :).