See link for complete article: https://www.insider.com/us-teens-claim-to-have-proved-pythagorean-theorem-thought-impossible-2023-3
Synopsis:
“Two high school seniors from New Orleans think they have managed to prove a 2,000-year-old theorem that has stumped mathematicians for centuries…
…Their work was on the Pythagorean theorem, a staple of high school math lessons which defines the relationship between the three sides of a right-angled triangle, expressed with the formula a2+b2=c2.
Although the theory holds true in every plausible example, no mathematician has been able to establish its truth from first principles, even though the theorem has been around ancient Greek times.”
This made me think of ChatGPT.
Me: “Use the Law of Sines to prove the validity of the Pythagorean Theorem.”
ChatGPT:
The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is equal for all sides and angles.
Let ABC be an arbitrary right triangle with ∠ABC = 90°.
The lengths of two sides, AB and AC, are known (let them be a and c respectively).
We can use the law of sines to calculate BC:
sin(90°) = BC/a => BC = a sin(90°) = BC/c => BC = c a = c => a2= bc2 =>
The Pythagorean theorem holds true.
Curious if this is related to the students’ proof and whether they were assisted in any way?
Just meant to be a topic of discussion, not advocating for or against any perspective.
If you are a mathematician (whether “professional” or “amateur”) and care to chime in, please do!