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New Orleans teenagers found a new proof of the Pythagorean Theorem

keith-mcnulty.medium.com

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Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#51

Post by kurthr »

oceansea wrote: post #24
ivan_gammel wrote: post #8

Earlier quoted context omitted.

Can you elaborate on what is a proof in your opinion? Having a degree in applied physics and mathematics from MIPT I’m struggling to understand your point. It does look like a proof of the theorem to me.

https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l... I am using Stanford University’s definition.

Ok, I have read the first 20 slides for a CS class at an institution from which I have a degree. I feel no closer to understanding why it is relevant.

Can you specify which step in the "new proof" is wrong, unproven, or tautological (itself requires the Pythagorean theorem)?

The simplest reason why it is explanatory as defined in your cited reference is that the Euclidean distance is defined by the hypotenuse of the triangle, that triangle (and similar triangles by construction) have ratios which are also similar, the distance along a side is the sum of those distances in an infinite series, the series expansions of sin and cosine are known along with the law of sines and are independently (from the Pythagorean) proven.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#52

Post by scythe »

joe_the_user wrote: post #20

I have read about this proof for a bit and this is the first write-up that gives the slightest details. The phrase "using trigonometry" is confusing. What they do is assume functions sine and cosine exist, as normally defined, as ratios of triangle values, without assuming these have the various Pythagorean-theorem derived properties. They then construct an infinite series of nested triangles and use the formula for…

Induction isn't so bad. I'm not sure how they're getting away with the Law of Sines, though. The usual proof of LoS that I know is dependent on the existence of the circumcircle. But I don't know how to prove the existence of the circumcircle without dragging in a lot of geometry. Or you can use the area formula, which makes the proof similar to other arguments that use the area formula.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#53

Post by varenc »

majormajor wrote: post #18
capableweb wrote: post #11

Earlier quoted context omitted.

"Here's How" is usually used for clickbait stuff and adds nothing of substance to the title itself. New Orleans Teenagers Found a New Proof of the Pythagorean Theorem is both shorter and less editorial than Here’s How Two New Orleans Teenagers Found a New Proof of the Pythagorean Theorem

I get why that's the default behavior but "adds nothing of substance" is a huge generalization that fails in this case. An article with zero details about the proof could easily be titled "New Orleans Teenagers Found a New Proof of the Pythagorean Theorem" but couldn't accurately be titled "Here’s How Two New Orleans Teenagers Found a New Proof of the Pythagorean Theorem." Whereas here it says it'll have more details…

This is getting off topic, but IMHO the HN default behavior here is reasonable.

There's certainly situations where removing the leading "Here's How" makes the title worse, but I think those instances are rare and in general this rule leads to better titles much more often than worse titles. Manual human review would of course be better, but dang only runs in O(n) time. Basically, it's not perfect but I think it does much more good than harm.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#54

Post by nolamark »

for completeness, here is a reference to the AMS presentation. https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Pa...

[my post updated to include abstract]

Abstract

In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#55

Post by boomboomsubban »

secondcoming wrote: post #17
HL33tibCe7 wrote: post #9

> By all accounts, these two teenage math students are the exact opposite of the majority of the math establishment. They are female, they are African-American, and they come from an area which is not particularly renowned for producing high academic achievers. This is just an awesome turn of events and one which should inspire anyone — no matter what their ethnic, gender or socio-demographic background — that excell…

I don’t think Privilege matters in all cases, look at the background of Ada Lovelace.

... The daughter of Lord Byron?

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#59

Post by uberman »

HL33tibCe7 wrote: post #9

> By all accounts, these two teenage math students are the exact opposite of the majority of the math establishment. They are female, they are African-American, and they come from an area which is not particularly renowned for producing high academic achievers. This is just an awesome turn of events and one which should inspire anyone — no matter what their ethnic, gender or socio-demographic background — that excell…

How would it be remiss to omit these factors, several of which seen irrelevant.

Are you suggesting that their proof be discounted because it might be divinely inspired?

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