2 HS students from NOLA shake up the world of math in a huge way... (2 Viewers)

[FullMonte]

That's what you consider, "In Short"?

LOL…I suspect it will be short compared to their method.

 

[longtime lurker]

Right on, congrats to them.

 

[mjcouvi]

I'm impressed with what is being reported, and I'm looking forward to reading their paper whenever it is published. But, I've also seen the Pythagorean theorem proved with geometry.

In short. Take a right triangle with sides a,b, and c. Make four copies, rotating each 90 degrees, and placing it so that the points are touching, and sides a of the copy and b of the previous triangle are in line with each other. This creates a square with sides of length a+b. Inside of this square is a smaller square with sides of length c (rotated a bit). The area of the large square is (a+b)^2. The area of each triangle is 1/2(ab). The area of the smaller square is c^2. The area of the large square is also equal to the sum of the areas of the four triangles and the smaller square, 4[ 1/2(ab)] + c^2 (which reduces to 2ab + c^2). This leaves us with (a+b)^2 = 2ab + c^2. Multiply out the left side, and we get a^2 + 2ab + b^2 = 2ab + c^2. Subtract 2ab from both sides, and you are left with a^2 + b^2 = c^2.

I don't have the patience to follow this, but I'm impressed with the patience it must've taken to write it out.

 

[FullMonte]

I don't have the patience to follow this, but I'm impressed with the patience it must've taken to write it out.

Wasn't too bad. After watching it, it made sense, and was easy to type out to explain. Here is a picture that makes it a little clearer.

 

[faceman]

Wasn't too bad. After watching it, it made sense, and was easy to type out to explain. Here is a picture that makes it a little clearer.

Math can be brutal. The last step of the scientific method is passing peer review

These young women did a great job using the law of sines.

A trigonometric proof of the Pythagorean theorem at last? The news said it was done by two high school students!

The latest mathematical news involves two high school students from New Orleans who have found a new way to prove the Pythagorean Theorem, which of course states that for a right triangle, the squa…

whyevolutionistrue.com

I'm going to bow out now because my head hurts.

Once again a tip of the cap to these young ladies.

 

[FullMonte]

Math can be brutal. The last step of the scientific method is passing peer review

These young women did a great job using the law of sines.

A trigonometric proof of the Pythagorean theorem at last? The news said it was done by two high school students!

The latest mathematical news involves two high school students from New Orleans who have found a new way to prove the Pythagorean Theorem, which of course states that for a right triangle, the squa…

whyevolutionistrue.com

I'm going to bow out now because my head hurts.

Once again a tip of the cap to these young ladies.

Oh definitely. As I said earlier, I'm thrilled to see our young people making strides like this, and I applaud them for what they appear to have done. I am looking forward to reading their paper when it comes out.

 

[Bleu Raeder]

Math can be brutal. The last step of the scientific method is passing peer review

These young ladies are impressive, I tip my cap to them.

My science fair projects in high school centered around three-dimensional geometry and the math of monkey saddles (https://en.wikipedia.org/wiki/Monkey_saddle) and pseudo-polyhedrons (https://en.wikipedia.org/wiki/Pseudo-uniform_polyhedron) including the ability to describe both closed and open systems. I can attest that peer review is brutal and unforgiving.

 

[Optimus Prime]

Two college freshmen who, during their final yearof high school, found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for generations thought was impossible – have since uncovered multiple more such proofs, they revealed in a national interview on Sunday.

“We found five, and then we found a general format that could potentially produce at least five additional proofs,” Calcea Johnson said on CBS’s 60 Minutes, a little more than a year after she and Ne’Kiya Jackson collaborated on an accomplishment that earned them international recognition.

Nonetheless, in comments that stunned their interviewer, Bill Whitaker, the two graduates of St Mary’s Academy in New Orleans denied seeing themselves as math geniuses and dismissed any interest in pursuing careers in mathematics.


“People might expect too much out of me if I become a mathematician,” Jackson said, shaking her head. Johnson, for her part, added: “I may take up a minor in math, but I don’t want that to be my job job.”

Sunday’s conversation on CBS’s popular Sunday evening news magazine were perhaps their most extensive, widely broadcast remarks to date on the new ground that they broke with respect to the Pythagorean theorem.…..

Teens who discovered new way to prove Pythagoras’s theorem uncover even more proofs

As high school students, Calcea Johnson and Ne’Kiya Jackson worked to find valid new proof for the 2,000-year-old theorem

www.theguardian.com

 

[efil4stnias]

 

[nolaspe]

Barkley, 'Those girls are not turrrrrrrrrrrible in the least bit!'

 

[Optimus Prime]

Two students who discovered a seemingly impossible proof to the Pythagorean theorem in 2022 have wowed the math community again with nine completely new solutions to the problem.

While still in high school, Ne'Kiya Jackson and Calcea Johnson from Louisiana used trigonometry to prove the 2,000-year-old Pythagorean theorem, which states that the sum of the squares of a right triangle's two shorter sides are equal to the square of the triangle's longest side (the hypotenuse).

Mathematicians had long thought that using trigonometry to prove the theorem was unworkable, given that the fundamental formulas for trigonometry are based on the assumption that the theorem is true.

Jackson and Johnson came up with their "impossible" proof in answer to a bonus question in a school math contest. They presented their work at an American Mathematical Society meeting in 2023, but the proof hadn't been thoroughly scrutinized at that point. Now, a new paper published Monday (Oct. 28) in the journal American Mathematical Monthly shows their solution held up to peer review. Not only that, but the two students also outlined nine more proofs to the Pythagorean theorem using trigonometry.

"To have a paper published at such a young age — it's really mind-blowing," Johnson, who is now studying environmental engineering at Louisiana State University, said in a statement emailed to Live Science. "I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things."

By proving Pythagoras' theorem using trigonometry, but without using the theorem itself, the two young women overcame a failure of logic known as circular reasoning. Trigonometry is a branch of mathematics that lays out how the sides, lengths and angles in a triangle are related, and as such, the discipline often includes expressions of the Pythagorean theorem. But Jackson and Johnson managed to prove the theorem using a result of trigonometry called the Law of Sines, dodging circular reasoning.

In the new study, and on top of their initial proof, the young mathematicians described four new ways to prove Pythagoras' theorem using trigonometry, as well as a novel method that revealed five more proofs, totaling 10 proofs.

Jackson and Johnson are only the third and fourth people known to have proven the Pythagorean theorem using trigonometry and without resorting to circular reasoning. The two other people were professional mathematicians, according to the statement..............

High school students who came up with 'impossible' proof of Pythagorean theorem discover 9 more solutions to the problem

In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school.

www.livescience.com

 

[Madmarsha]

Are they getting the Nobel? They need to get the Nobel.

 

[where yat brah]

More likely the Fields medal and/or Abel Prize. There isn't a Nobel for math.

 

[livefromDC]

More likely the Fields medal and/or Abel Prize. There isn't a Nobel for math.

I only knew this because of Good Will Hunting.

 

[Madmarsha]

More likely the Fields medal and/or Abel Prize. There isn't a Nobel for math.

I know even less about math than I thought.