This is what I do, lol. I tell my friends I'm gonna walk the hypotenuse so I can walk less.

Pythagoras = Others

Bro acting like Pythagoras discovered the triangle inequality

If building one side of the square road takes 190 bricks, how many bricks takes to build the desired path?

People who ask these types of questions don’t understand it enough to use it in the real world.

The Pythagoean theorem is probably one of the most equations in all of math, science, engineering, data analysis, etc. It essentially tells you how to measure distance in a multidimensional space. Any time you do anything with two or more variables, this is relevant.

Indeed. To work out the distance between map co-ordinates.

I'm an engineer, so quite often.

Used in machining, looking at 3D objects usually a part that’s going to be turned(machine operation). It helps when looking at concentricity of multiple diameters along the same center line.

When building a fence.

Yes but I build stuff so…

Checking if something is squared. For example, if you measure 3’ from one corner and 4’ from the other corner and you measure from the 2 lengths if it’s square it will equal 5’

The 3 4 5 method is an old school technique in construction

So there are quiet a few quadratic functions in physics. E.g. if you have free fall (time is quadratic there) or gravity and electromagnetism. But really the reason you have it in the curriculum is, its pretty much the last polynomial you can solve easily by hand, so a lot of approx. And techniques boil down to get it at least to a quadratic equation and solve that.

Everything is a harmonic oscillator if you're brave enough.

Whenever you want to study (small) perturbations out of an equilibrium, you will almost certainly end up with a quadratic equation somewhere.

My favourite use is solving 2nd order partial differential equations to yield a complex number that provides the frequency and damping factor of a damped harmonic oscillator.

This is awesome! This is exactly the kind of answer that kids need to that question. Keep up the good work!

I think there is unlikely to be a satisfying answer to this question, although I cannot rule out the possibility.

Every proof I have seen of Pythagoras' theorem is essentially in one of three categories.

1. Purely geometric proofs.
2. Proofs that exploit properties of the sine and cosine functions.
3. Sleight of hand arguments about metrics induced by inner products.

I will focus on only the first, because it seems most relevant to your question. Among geometric proofs there are essentially two avenues of approach.

The first avenue argues from the scaling properties of area (a contraction by a reduces area by a^(2)**). Area is an essentially two dimensional phenomenon so in three dimensions this would have to focus on surface areas.

The second avenue chases two pairs of similar figures, to show some segment is composed of copies of itself scaled by a twice and b twice, respectively. An argument of this type in three dimensions would involve looking at lines and angles, so care would need to be taken that it does not reduce to a two dimensional argument.

You may be interested in this collection of 122 geometric proofs of the Pythagorean theorem, non of which extend beyond the plane.

Lastly, you mentioned dissections of 3d shapes so this closely related problem might be relevant. Is there a 3d polyhedron that can be dissected into two pieces similar to itself? The first geometric proof of Pythagoras would apply here also, and yield a^(3)**+b*^(3)=c^(3)**.*

I'm not aware of any proof like that. But I also think you might be wasting your time looking for one.

Sometimes a statement about objects in one number of dimensions can be proven by adding dimensions. There are two situations I can think of where that's interesting:

1. if the statement becomes considerably easier/more intuitive to prove if you add more dimensions (this suggests that the statement might have been about higher dimensions all along)
2. if the statement is well known but it appears as a surprise corollary within a completely different context

The usual proofs of the Pythagorean theorem that work by cutting up squares and moving the pieces around are very simple. That means Option 1 is out of the picture.

Option 2 can't really be planned for. Either you do work in some unrelated theory and suddenly the Pythagorean theorem pops up, or not.

I don't know... musing out loud, but a cone is solid of revolution of a right triangle. Any relationships in a cone that would imply the pythagorean theorem?

I think you should pursue it. This sounds interesting.

Does the Riemann sphere count? Since on the sphere straight lines become circles, the rank 2, three term Grassmann-Plücker relation proves Ptolemy which proves Pythagoras. 

The ladder problem is of the classic "Solve Pythagoras' Theorem so that a, b, and c are all integer values".

Hey /u/SENDUNE!

If your post is a screenshot of a ChatGPT conversation, please reply to this message with the conversation link or prompt.

If your post is a DALL-E 3 image post, please reply with the prompt used to make this image.

Consider joining our public discord server! We have free bots with GPT-4 (with vision), image generators, and more!

🤖

Note: For any ChatGPT-related concerns, email support@openai.com

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

I heard he actually never did this, because he knew the hypotenuse was irrational.

My friends in college used to say “hit up the hypotenuse” to refer to doing exactly this lol

Patron Saint of desire paths?

Can’t upvote, 1.111 upvotes!

I think of Pythagoras every time I cut a corner

https://preview.redd.it/jrgelza3cyye1.jpeg?width=3072&format=pjpg&auto=webp&s=0b5f8154df0699fb5f5c49d435acd6911ba9b0bd

This is Pythagoras, he approves!

C² = A² + T² : )

Is that a right angled triangle? Because it sure looks acute.

Perfectly straight hypote-mews 📐🐈‍⬛

What a smart voidling 🖤

Hi u/terobaaau,

This is an automated reminder from our moderators. Please read, and make sure your post complies with our rules. Thanks!

Please be sure to explain the steps you have tried to solve the problem. Asking for help is okay, asking for the solution is not.

If your post consists of only a math problem, without showing effort on your part, it will be removed. Please follow the rules and sidebar information on 'how to ask a good question'

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.