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re: New Orleans East teens make 'impossible' mathematical discovery unproven for 2,000 years
Posted on 3/24/23 at 6:20 pm to NPComb
Posted on 3/24/23 at 6:20 pm to NPComb
quote:
Therefore, Pythagoras' Theorem can be proven using geometry.
Here is another proof using algebra and geometry. There are many more, I'm sure. It's better with drawings of the squares and triangles, but when I first saw it I thought it was pretty elegant.
1. Consider a square with sides of x
length.
2. The area of that square is x^2.
3. Divide each side of that square into
two line segments a & b, so (x=a+b).
4. The area of the square can now be
written in terms of a+b in place of
x. The area is therefore a^2+2ab+b^2.
5. Each corner of the original square
can be used to create a right
triangle by connecting the endpoints
of each segment a and b, creating
another line segment, c.
6. Therefore the original square has
been divided into 4 identical right
triangles each with sides a, b, and
c, plus a smaller square with sides
equal to c.
7. The area of each of the 4 right
triangles is ab/2, and the area of
the smaller square is c^2.
8. The sum of the area of the smaller
square and the areas of the 4 right
triangles must be equal to the area
of the original square which they are
contained within (the sum of the
parts must equal the whole).
9. Therefore a^2+2ab+b^2=c^2+4ab/2.
10. 4ab/2=2ab, so we can subtract 2ab
from both sides of the above
equation. That leaves us with
a^2+b^2=c^2.
2
Posted on 3/24/23 at 6:23 pm to DoItDoug
quote:not when St. Mary’s Academy was mentioned in the first sentence
Am I the only one who pictured two Vietnamese girls from N O East
Posted on 3/24/23 at 6:23 pm to REG861
quote:
“ a black person is getting positive recognition . Quick, everyone panic!”-
What is recognition for - just presenting or actually proving 2000 years of math incorrect? And how was it earned?
The interests in math and in education are great things, but it would be foolish to not think that race and location played a part in these being only high schoolers presenting and to not think circular logic is still present.
Articles should focus on presentation and experience. Students should also be a little more focused on those and continuing process with peer reviews instead of talking like they proved what was presented just by presenting. That should be part of their education and learning process. These are high schoolers not elementary students.
Instead some like WWL are going with a non-peer reviewed presentation to a Math group as:
quote:
” New Orleans East teens make 'impossible' mathematical discovery unproven for 2,000 years”
What they were able to do is find a way to prove the theory using trigonometry WITHOUT circular logic -- something mathematicians have been trying to do for nearly 2,000 years.
… And even if you don't understand their math, it's easy to see that with the right push, students can do the impossible.
WWL article is written more in manner I see for elementary and middle schoolers who aren’t claiming to disprove 2000 years of math or circular logic or maybe a school newsletter. Even these usually state why or how students were chosen to present along with some of their presentation showing their actual work.
The guardian article was written better, and I think showed reason why presentation happened in first place.
quote:
“US teens say they have new proof for 2,000-year-old old mathematical theorem”
…Catherine Roberts, executive director for the American Mathematical Society, said she encouraged the St Mary’s students to see about getting their work examined by a peer-reviewed journal, even at their relatively young age.
“Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature,” said Roberts, whose group hosts scientific meetings and publishes research journals.
Roberts also said American Mathematical Society members “celebrate these early career mathematicians for sharing their work with the wider mathematics community”.
“We encourage them to continue their studies in mathematics,” Roberts added.
Posted on 3/24/23 at 7:07 pm to dallastigers
I encourage them to consider their studies too, but I still haven't seen or had described to me specifically what they accomplished.
Pythagoras, Fermat, and Beal (who has a million dollar bounty for a proof on a closely related problem) all considered this problem in depth, and the writer of this article seemed to want to build up the young ladies more than explain what they have supposedly done.
I'm suspicious of the reporting.
Pythagoras, Fermat, and Beal (who has a million dollar bounty for a proof on a closely related problem) all considered this problem in depth, and the writer of this article seemed to want to build up the young ladies more than explain what they have supposedly done.
I'm suspicious of the reporting.
Posted on 3/24/23 at 7:37 pm to Tupelo
quote:
Here is another proof using algebra and geometry. There are many more, I'm sure. It's better with drawings of the squares and triangles, but when I first saw it I thought it was pretty elegant.
I agree this is a very elegant solution.
Posted on 3/24/23 at 7:44 pm to crap4brain
From ChatGPT
Yes, the Pythagorean theorem can be proved without using trigonometry. Here is one way to prove it:
Consider a right triangle with legs of length a and b and a hypotenuse of length c, as shown below:
css
Copy code
/|
/ |
c / | a
/___|
b
We want to show that a^2 + b^2 = c^2.
First, draw a square with sides of length c:
markdown
Copy code
__________
| |
| |
| |
|__________|
Divide the square into four congruent right triangles by drawing a diagonal:
bash
Copy code
__________
|\ /|
| \ / |
| \ / |
|___\__/___|
Note that each right triangle in the square is congruent to our original right triangle, since they have the same angles and one pair of matching sides (the hypotenuse). Therefore, the areas of these triangles are also equal.
The area of the square is c^2, and the area of each right triangle is 1/2 ab (since the base and height of each triangle are a and b). Therefore, the total area of the four right triangles is 2ab.
Since the area of the square is equal to the sum of the areas of the four right triangles, we have:
c^2 = 2ab
Dividing both sides by 2, we get:
a^2 + b^2 = c^2
which is the Pythagorean theorem.
So, we have proved the Pythagorean theorem without using trigonometry.
Yes, the Pythagorean theorem can be proved without using trigonometry. Here is one way to prove it:
Consider a right triangle with legs of length a and b and a hypotenuse of length c, as shown below:
css
Copy code
/|
/ |
c / | a
/___|
b
We want to show that a^2 + b^2 = c^2.
First, draw a square with sides of length c:
markdown
Copy code
__________
| |
| |
| |
|__________|
Divide the square into four congruent right triangles by drawing a diagonal:
bash
Copy code
__________
|\ /|
| \ / |
| \ / |
|___\__/___|
Note that each right triangle in the square is congruent to our original right triangle, since they have the same angles and one pair of matching sides (the hypotenuse). Therefore, the areas of these triangles are also equal.
The area of the square is c^2, and the area of each right triangle is 1/2 ab (since the base and height of each triangle are a and b). Therefore, the total area of the four right triangles is 2ab.
Since the area of the square is equal to the sum of the areas of the four right triangles, we have:
c^2 = 2ab
Dividing both sides by 2, we get:
a^2 + b^2 = c^2
which is the Pythagorean theorem.
So, we have proved the Pythagorean theorem without using trigonometry.
Posted on 3/24/23 at 8:16 pm to Tupelo
quote:
Consider
Makes me miss Coolidge.
Posted on 3/24/23 at 8:19 pm to Bestbank Tiger
quote:
Consider
Makes me miss Coolidge
CRIMINALLY underrated poster
Posted on 3/24/23 at 8:24 pm to crap4brain
Well if they wanted a ticket to just about any school they wanted to choose from, that’s an easy way to make that happen.
When you start solving unsolvable problems, you pretty much get accepted where you want to go
When you start solving unsolvable problems, you pretty much get accepted where you want to go
Posted on 3/24/23 at 8:58 pm to Alyosha
quote:
Yep, this is marketing at best. The article highlights what they presented, not what they’ve proven.
Maybe it's poor journalism because the reporting couldn't really understand what they did
Posted on 3/24/23 at 9:03 pm to Hammond Tiger Fan
quote:
Maybe it's poor journalism because the reporting couldn't really understand what they did
They did nothing. 2000 years ago Pythagoras did the same thing. It's how he came up with it.
Posted on 3/24/23 at 9:19 pm to crap4brain
I’m not sure which is worse - the article or the replies in this thread. Both are quite embarrassing.
The Guardian covers it better. The girls’ work is pretty impressive, and it’s not shocking the smooth brains around here are confused.
The Guardian covers it better. The girls’ work is pretty impressive, and it’s not shocking the smooth brains around here are confused.
Posted on 3/24/23 at 9:25 pm to crap4brain
Serious question-
Could they be awarded the Noble Prize for this discovery?
Edit***
I looked it up.
There is no Noble Prize for mathematics. The Abel Peize is the highest and comes with a $7.5M award.
Could they be awarded the Noble Prize for this discovery?
Edit***
I looked it up.
There is no Noble Prize for mathematics. The Abel Peize is the highest and comes with a $7.5M award.
This post was edited on 3/24/23 at 9:29 pm
Posted on 3/24/23 at 9:29 pm to bird35
Math is for losers
Posted on 3/24/23 at 9:33 pm to SquatchDawg
Is this like the funny movie when the sassy black ladies sent the rockets to the moon?
Posted on 3/24/23 at 9:51 pm to slackster
quote:
I’m not sure which is worse - the article or the replies in this thread. Both are quite embarrassing.
The Guardian covers it better. The girls’ work is pretty impressive, and it’s not shocking the smooth brains around here are confused.
I mentioned guardian covering it better, but I am still really not seeing work or how they got to present to truly label anything in regards to those as being impressive. I may have a blocker on that is stopping me from seeing more than their abstract on the meetings site, but I can’t that check right now.
Is there a file covering more than abstract and how they got to somehow present at this conference?
Posted on 3/24/23 at 10:02 pm to crap4brain
This is such BS. no teenager anywhere gives a shite about pythogora’s thereom. Give me a break. This was all orchestrated to make it look like two young black girls are these brilliant progidies that need to be revered. Who was really behind all this.
Let’s not pretend that some reporter just stumbled upon these two kids doing math problems at the picnic table in a park.
Let’s not pretend that some reporter just stumbled upon these two kids doing math problems at the picnic table in a park.
Posted on 3/24/23 at 10:11 pm to crap4brain
Their fathers must be proud…
Posted on 3/24/23 at 10:28 pm to theantiquetiger
The Fields Medal only pays like 15-20k, but is considered a mega high honor in mathematics.
Posted on 3/24/23 at 10:47 pm to Obtuse1
I’m skeptical after asking ChatGPT about this:
quote:
The formula sin^2x + cos^2x = 1 is known as the Pythagorean Identity in trigonometry, and it is often used in solving trigonometric equations and proving trigonometric identities. However, it is not related to the Pythagorean Theorem, which is a statement about the relationship between the sides of a right-angled triangle.
The Pythagorean Identity can be proved using the unit circle or the definitions of sine and cosine functions.
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