Pythagorean theorem water demo
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it as a quick, visual, physical demonstration of the Pythagorean theorem's area interpretation.
Recommended by 2 people across 2 different months, 2014 to 2019.
What it is
A 44-second clip showing a wheel-shaped container of liquid that demonstrates the Pythagorean theorem physically. Water poured between the square cavities on the sides of a right triangle shows that the two smaller squares fill the largest one. It was filmed at Brentwood and posted without narration.
What people said
Recommends Maxim Umansky · 2014-04 · Mathematics Stack Exchange · on “Visually stunning math concepts which are easy to explain”
Here is a very insightful waterproof demonstration of the Pythagorean theorem. Also there is a video about this [this video] . It can be explained as follows. We seek a definition of distance from any point in $\mathbb{R}^2$ to $\mathbb{R}^2$ , a function from $(\mathbb{R}^2)^2$ to $\mathbb{R}$ that satisfies the following properties. For any points $(x, y)$ and $(z, w)$ , $d((x, y), (x + z, y + w)) = d((0, 0), (z, w))$ For any point $(x, y)$ , $d((0, 0), (x, y))$ is nonnegative For any nonnegative real number $x$ , $d((0, 0), (x, 0)) = x$ For any point $(x, y)$ , $d((0, 0), (x, -y)) = d((0, 0), (x, y))$ For any points $(x, y)$ and $(z, w)$ , $d((0, 0), (xz - yw, xw + yz)) = d((0, 0), (x, y))d((0
Recommends Charlie · 2019-03 · Mathematics Stack Exchange · on “Looking for a conceptual proof of the pythagorean theorem from first principles”
The Pythagorean Theorem is a mathematical concept, so the first principles proof you're looking proof will necessarily come from mathematical axioms. However, if what you want is a more physical interpretation, this video could help you: [this video]
Cites user307169 · 2017-02 · Mathematics Stack Exchange · on “Pythagorean Theorem intuition”
What's bothersome about appealing to the notion of area for a theorem about angles and length? I'm surprised that would bother anyone with a pure math degree since such a person must have encountered several such proofs (i.e., proofs using ideas not found in the statement). Also, $a^2 + b^2 = c^2$ can be interpreted as a statement about areas [this video] since all three terms represent the areas of squares whose sides coincide with the sides of the triangle. Also, what are you asking exactly? For an intuitive way of thinking about the Pythagorean theorem?