I made a Mathematical Discovery!!!???

DarkDusk

Hi,
I think I made a mathematical discovery! It is to do with ratios and I was wondering what I should do?? Is there anyone very familiar with ratios and proportion?? Should I patent it?? (lol) By the way I'm a Junior cert student and I'm far from a maths guru! Help would be greatly appreciated.

Thanks,
James.

partyatmygaff

Before you get disappointed, it's probably nothing new. What is it incidentally?

DarkDusk

I made the discovery during maths class my accident.. I told my teacher and she made me come up to the board and do it out. She apparently didn't see it before..?? I also used the method when it came up in the mocks and I got full marks!!

click_here!!!

Ooh, intriguing. Don't tell us what it is! ;D

partyatmygaff

DarkDusk wrote: »

I made the discovery during maths class my accident.. I told my teacher and she made me come up to the board and do it out. She apparently didn't see it before..?? I also used the method when it came up in the mocks and I got full marks!!

What is it?

Fremen

You can't patent a mathematical result, or even an algorithm. If you have a new result, you can write a paper about it and submit it to a maths journal.

I don't mean to be harsh, but it's almost impossible for a student to stumble on a new discovery by accident, especially in an elementary field like fractions.

A small number of very talented secondary school students have been able to make contributions to mathematical research, but it takes an incredible amount of hard work. If you've come up with a result within a couple of hours, chances are someone out there knows it.

DarkDusk

I fully aware of what you are saying. I just thought it would be worth the shot because the method is totally random. At the same time it's so much shorter and easier than the normal method in our textbooks.

I'll just give you the question:
If x:y = 3:1 and y:z = 2:5, find the ratio x:z

Even if it has been discovered before it may be a good idea to put it into a future maths textbook for the JC. Just a thought....;)

im invisible

x:y:z = 6:2:5 ??
x:z = 6:5

so you multiply the ratios(fractions), top by top, bottom by bottom?
(is that how you normally do it, i cant even remember...)

Delphi91

DarkDusk wrote: »

...I just thought it would be worth the shot because the method is totally random...

That doesn't sound very promising!

Fremen

DarkDusk wrote: »

I fully aware of what you are saying. I just thought it would be worth the shot because the method is totally random. At the same time it's so much shorter and easier than the normal method in our textbooks.

I'll just give you the question:
If x:y = 3:1 and y:z = 2:5, find the ratio x:z

Even if it has been discovered before it may be a good idea to put it into a future maths textbook for the JC. Just a thought....;)

Express them as fractions and multiply them (so (3/1)X(2/5) = 6/5 ), maybe? I don't know how you're taught to do this in school.

I know from experience that when you think you've made a big discovery, your first instinct is to keep it secret so that no-one will steal your idea. That's probably counterproductive, especially at student level. If you tell us what you're thinking, we might be able to give you some feedback.

Ficheall

I remember the summer after primary school discovering that x^2-y^2 could easily be solved by (x+y)*(x-y). Was delighted and informed my dad who congratulated me but informed me that sadly the discovery had already been made by someone else

DarkDusk

I guess I was getting ahead of myself...:( Yes the multiplying out topxtop and bottomxbottom was it. I dunno why I thought it was a "discovery". I guess since my teacher got me up to do it and all. It just tells me how s*!* of a teacher she is!! Can't believe she didn't notice it was so basic math and easy. The method in our book and the one she taught us is so different and complicated.. Anyway, sorry for wasting your time..:(

Learning different ways of doing these problems is a good thing, don't forget your sense of discovery and keep playing around with them!

DarkDusk

bluewolf wrote: »

Learning different ways of doing these problems is a good thing, don't forget your sense of discovery and keep playing around with them!

Thanks! My teacher is soooo misleading. Thanks god she is retiring next year!!!

Fremen

DarkDusk wrote: »

I guess I was getting ahead of myself...:( Yes the multiplying out topxtop and bottomxbottom was it. I dunno why I thought it was a "discovery". I guess since my teacher got me up to do it and all. It just tells me how s*!* of a teacher she is!! Can't believe she didn't notice it was so basic math and easy. The method in our book and the one she taught us is so different and complicated.. Anyway, sorry for wasting your time..:(

Well, don't beat yourself up. You've done one better than your textbook, which is an accomplishment in itself. It shows a capacity for independent, creative thought. If that's the one thing you take away from secondary education, you're still doing pretty well.

DarkDusk

Thank you for being so supportive!

bnt

Here's another way of looking at it, in algebraic terms:
"x:y = 3:1 and y:z = 2:5, find the ratio x:z"

The variable that's common to both inputs is y, but it's not part of the result you want, so you want to eliminate it. You can do this by rearranging each of the inputs so it's in terms of y, then put them together as y=y:

1) x/y=3/1 => y/x = 1/3 => y=x/3
2) y/z=2/5 => y=2z/5

y=y, so x/3 = 2z/5 => x/z = 6/5
or x:z = 6:5 in ratio form.

This might look like overkill, and Fremen's method is easier in this case, but these things can get a lot more complicated later! :cool:

LeixlipRed

Definitely no reason to get glum about it, I'm sure many of the posters on here delighted in besting their teacher or the text books, that's an achievement in itself. The most important thing is to always ask yourself, why does my method work? What's different about it? Are they actually the same thing? So on, so forth, always having an open mind is the most important thing.

And feel free to come on here and discuss anything mathematical with us in future!

Professor_Fink

DarkDusk wrote: »

I guess I was getting ahead of myself...:( Yes the multiplying out topxtop and bottomxbottom was it. I dunno why I thought it was a "discovery".

Don't worry. A large part of my job is in coming up with new proofs, and even now I end up reinventing the wheel fairly often. Just because this wasn't new shouldn't put you off trying to find new ways to solve problems.

moycullen14

Good man, stick at it, keep thinking about problems and how to solve them.

In programming there is a language called Perl whose motto is 'There is more than one way to do it', shortened to TMTOWTDI, pronounced TIM TOADY. It is a very important part of computer theory - the idea that there are more efficient ways to solve problems - at least it used be when resources were scarce.

My son came back from school recently with the very same problem (in fact the numbers were probably the same), in terrible knots about how to solve it. When showed the variable method above (y=2/5z, etc), he couldn't believe how complicated it had been made and how simple it was. Teachers really miss a trick by not showing kids different approaches to problem solving - the real world benefit of maths.

I remember a great teacher of mine going through co-ordinate geometry using polar notation to show how some things were easier (and some almost impossible) to find (distance between points, areas of triangles, etc) using a particular notation. The idea that a point can be represented in 2D by either an x,y co-ord or an angle/distance pair, I think, really helps with understanding the concepts.

FoxT

Well done, DarkDusk. Don't worry if it was already known - the fact that you figured out how to do this independently is great.

-FoxT

fergalr

moycullen14 wrote: »

In programming there is a language called Perl whose motto is 'There is more than one way to do it', shortened to TMTOWTDI, pronounced TIM TOADY. It is a very important part of computer theory - the idea that there are more efficient ways to solve problems - at least it used be when resources were scarce.

Whether TMTOWTDI, as applied in Perl, is a good thing, is controversial among programmers.

I also wouldn't agree with your interpretation of it; its not really the idea that there are different (possibly more efficient) ways to solve problems - its more the idea that a particular programming intention can be expressed in many ways.


All that said, the general idea in the thread, that its good to question things, and try find different and better ways of solving problems, is great.

Pygmalion

fergalr wrote: »

I also wouldn't agree with your interpretation of it; its not really the idea that there are different (possibly more efficient) ways to solve problems - its more the idea that a particular programming intention can be expressed in many ways.

Indeed, I always interpreted it as "There is more than one way to implement the same algorithm" rather than "There is more than one algorithm to solve a problem", it's obvious that the latter must be accounted for, but it could be argued that a programming language that provides for the former could be a source of confusion.

I think the point being made in this case though was that it's often more educational to see multiple way of doing things (even if in theory they're all equivalent and you're just representing the data differently or doing things in a different order).
Often if you're having trouble with a concept a different explanation (or even a different algorithm entirely) can help you to understand "why" it works and help it click.

Probably getting a bit off topic though :P