2 HS students from NOLA shake up the world of math in a huge way... (1 Viewer)

[Dago]

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.

 

[guidomerkinsrules]

I only knew this because of Good Will Hunting.

it's not your fault

 

[Nisey55]

it's not your fault

So it's your fault?

 

[guidomerkinsrules]

So it's your fault?

Usually

 

[DCSaints_Fan]

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

This is very, very far from Fields medal worthy

 

[Bleu Raeder]

This is very, very far from Fields medal worthy

I think you're likely very right about this.

I have seen some discussions in math circles (yes, there are math circles I travel in) that some of the proofs may need much more work in order to verify uniqueness without circular logic. Initial peer review of the original work was well-done but was not widespread. There is a lot to be discussed and argued about the proofs they have developed.

REGARDLESS - these young ladies have been brilliant and methodical in their approach and have caused a truckload of discussion. In and of itself, their recognition and awards have been appropriate so far.

 

[DCSaints_Fan]

I think you're likely very right about this.

I have seen some discussions in math circles (yes, there are math circles I travel in) that some of the proofs may need much more work in order to verify uniqueness without circular logic. Initial peer review of the original work was well-done but was not widespread. There is a lot to be discussed and argued about the proofs they have developed.

REGARDLESS - these young ladies have been brilliant and methodical in their approach and have caused a truckload of discussion. In and of itself, their recognition and awards have been appropriate so far.

I know I'm right, since anything Fields medal worthy, would not be able to be comprehended by me

I've read it a few times ... while I don't think its complete nonsense I'm really failing to see the real impact. There have been hundreds of proofs, many of which are much more intuitive and do not involve trig, only geometric constructions and algebra (which they also use)

I might do a full takedown of the paper if I feel up to it

 

[Bleu Raeder]

I know I'm right, since anything Fields medal worthy, would not be able to be comprehended by me

I've read it a few times ... while I don't think its complete nonsense I'm really failing to see the real impact. There have been hundreds of proofs, many of which are much more intuitive and do not involve trig, only geometric constructions and algebra (which they also use)

I might do a full takedown of the paper if I feel up to it

I'll look forward to that!

As in many things math-related, there may not be any impact outside of new or novel proofs, but you know that. When I was working on my math project many years ago, I wanted to find practical implications and struggle to do so to this day. Among those much smarter than I, I asked the questions of practicality over and over again with no real answers.

 

[livefromDC]

I know I'm right, since anything Fields medal worthy, would not be able to be comprehended by me

I've read it a few times ... while I don't think its complete nonsense I'm really failing to see the real impact. There have been hundreds of proofs, many of which are much more intuitive and do not involve trig, only geometric constructions and algebra (which they also use)

I might do a full takedown of the paper if I feel up to it

Perhaps this too is something you don't comprehend. After all, you're missing the fundamental point of their proof. The entire stated point of their proof is that they were able to prove the Pythagorean Theorem using trigonometry without circular logic. So you're going to do a "full takedown" of a paper written by high school kids for what? Because it set out to use trig? The fact that "there have been hundreds of proofs, many of which are much more intuitive and do not involve trig, only geometric constructions" has nothing to do with what they were trying to prove.

So while you're at it, can you do a "full take down" of Grant Holloway's gold medal in 110 meter hurdles in 12.99s because there have been hundreds of people who've ran the 100 meters in under 10 seconds!

Do you, guy. But wanting to take down a couple of high school girls when the rest of the world is lauding their efforts just sounds miserable. You took their work and likened it to nonsense, smh. Sigh, but go ahead put them in their place.

 

[livefromDC]

So your answer to high schoolers not getting enough credit in the media for their math accomplishments is to negate the math accomplishments of these 2 local high schoolers getting credit in the media.

The track analogy was to point out that your criticism was for a race they weren't trying to run, solving the theorem without using trig.

 

[guidomerkinsrules]

So your answer to high schoolers not getting enough credit in the media for their math accomplishments is to negate the math accomplishments of these 2 local high schoolers getting credit in the media.

The track analogy was to point out that your criticism was for a race they weren't trying to run, solving the theorem without using trig.

you seem to be saying his critique...doesn't add up

 

[DCSaints_Fan]

The track analogy was to point out that your criticism was for a race they weren't trying to run, solving the theorem without using trig.

No, thats not what they did.

Many non-trigonmetric proofs of Pythagorean theorem exist.

What they are trying to show is a trigonometric proof of the Pythagorean theorem, that does not involve circular reasoning i.e., contain the Pythagorean theorem as one of its implicit assumptions.

 

[DCSaints_Fan]

Ok I'm going to go ahead and do a more in depth dive into this one. First I'll handle some preliminaries before I go into the details of the paper. So please excuse the long-windedness of this post - which I'm going to break up into several parts.

The claim in the paper (its right in the abstract) is they can prove Pythagorean theorem (a^2 + b^2 = c^2, where a, b, and c are the sides a right triangle), using trigonometry.

Part I - Preliminaries

What is a proof? In the mathematical context, it means showing a mathematical statement to be true, based on other true statements.

When constructing mathematics, you have to start somewhere - in other words you have to assume certain statements are true. These are usually called axioms, postulates and in a certain form definitions.

They are also terms which lack a definition. e.g. in plane geometry, point line and plane. Although we have an intrinsic conception of what these are (a point is a "dot", a line is a "inifite collection of points between two points that is contiguous and straight" ), since the language of math should be precise, if you can't do that its best to leave them undefined. "Number" is another example - we simply just "know" what a number is without having to provide a definition.

Also existing somewhat parallel to these axioms, are the "rules" of logic. These include ideas such as "if a statement P (aka predicate) is true, and P implies Q, then Q must also be true" and "if P implies Q (is true), and Q is false, then P is also false". Since these permeate every branch of mathematics, they are often simply assumed.

By starting with the axioms, together with rules of logic, we can construct new true statements, we didn't know before. This is called a proof. These new true statements are generally called theorems (sometimes lemmas or corollaries)

The theorems of geometry can be constructed assuming only five axioms, given by Euclid. I would note these postulates assume that certain terms like point, line, circle and angle are already understood.

Of particular interest in our case, is the third postulate having to do with the a circle. "Given any straight lines segment, a circle can be drawn having the segment as radius and one endpoint as center". Also the fourth postulate - "all right angles are concgruent". doesn't define right angle or even angle.

Now in terms out, you can define a circle as a "set of points equidistant from some center point".

Similarly, you can also define angle as something like the "length of the circular segment on a circle of radius 1 when intersected by two lines with a common origin at the center of the circle"

But in order to do that, we already have used the terms "length" and "equidistant". These are measures of geometric objects, in this case line segments. While not pure geometric ideas, in order to do anything much useful in geometry you need to introduce them.

So when we say something like the "length of the line segment AB is equal to the length of the line segment BC", what we mean is the number assigned to the measure of each of them is equal. For now assume the numbers obey the standard rules of algebra. e.g. if a = b then a + c = b + c, etc.).

(to be continued)

 

[Bleu Raeder]

Ok I'm going to go ahead and do a more in depth dive into this one. First I'll handle some preliminaries before I go into the details of the paper. So please excuse the long-windedness of this post - which I'm going to break up into several parts.

The claim in the paper (its right in the abstract) is they can prove Pythagorean theorem (a^2 + b^2 = c^2, where a, b, and c are the sides a right triangle), using trigonometry.

Part I - Preliminaries

What is a proof? In the mathematical context, it means showing a mathematical statement to be true, based on other true statements.

When constructing mathematics, you have to start somewhere - in other words you have to assume certain statements are true. These are usually called axioms, postulates and in a certain form definitions.

They are also terms which lack a definition. e.g. in plane geometry, point line and plane. Although we have an intrinsic conception of what these are (a point is a "dot", a line is a "inifite collection of points between two points that is contiguous and straight" ), since the language of math should be precise, if you can't do that its best to leave them undefined. "Number" is another example - we simply just "know" what a number is without having to provide a definition.

Also existing somewhat parallel to these axioms, are the "rules" of logic. These include ideas such as "if a statement P (aka predicate) is true, and P implies Q, then Q must also be true" and "if P implies Q (is true), and Q is false, then P is also false". Since these permeate every branch of mathematics, they are often simply assumed.

By starting with the axioms, together with rules of logic, we can construct new true statements, we didn't know before. This is called a proof. These new true statements are generally called theorems (sometimes lemmas or corollaries)

The theorems of geometry can be constructed assuming only five axioms, given by Euclid. I would note these postulates assume that certain terms like point, line, circle and angle are already understood.

Of particular interest in our case, is the third postulate having to do with the a circle. "Given any straight lines segment, a circle can be drawn having the segment as radius and one endpoint as center". Also the fourth postulate - "all right angles are concgruent". doesn't define right angle or even angle.

Now in terms out, you can define a circle as a "set of points equidistant from some center point".

Similarly, you can also define angle as something like the "length of the circular segment on a circle of radius 1 when intersected by two lines with a common origin at the center of the circle"

But in order to do that, we already have used the terms "length" and "equidistant". These are measures of geometric objects, in this case line segments. While not pure geometric ideas, in order to do anything much useful in geometry you need to introduce them.

So when we say something like the "length of the line segment AB is equal to the length of the line segment BC", what we mean is the number assigned to the measure of each of them is equal. For now assume the numbers obey the standard rules of algebra. e.g. if a = b then a + c = b + c, etc.).

(to be continued)

Is your last name Runnels, by any chance?

 

[livefromDC]

No, thats not what they did.

Many non-trigonmetric proofs of Pythagorean theorem exist.

What they are trying to show is a trigonometric proof of the Pythagorean theorem, that does not involve circular reasoning i.e., contain the Pythagorean theorem as one of its implicit assumptions.

You're really struggling with that analogy. Read it again, that's exactly what I said. Of course it's not what they did or what they were setting out to do. You criticized them for doing a proof using trig by comparing it to the people who proved the theorem without using trig.

Based on your earlier post, it seems you're just catching on to that fact and trying to change your tune. At any rate, I have no faith you will correctly interpret their proof.