Omg Sin And Cosine Have Been Eliminated

K.I.L.E.R

Retarded moron
Veteran
http://www.physorg.com/news6555.html

Seriously this is THE breakthrough of the century.
This rewrites all of the important rules of mathametics.

It's simpler so it means computers will be doing less work when it comes to calculating angles.

Oh wait, never mind.
He's just replaced the concepts and is using algebra to solve the problems.
Might not be a good idea to use the concept within computing(performance wise).
 
K.I.L.E.R said:
[Omg Sin And Cosine Have Been Eliminated

No Sine and Cosine have not "been eliminated". When I did analysis at Uni', Sin and Cos were defined to be solutions to

d/dx(f(x)) = g(x)
d/dx(g(x)) = -f(x)

The fact that you can use them to measure angles and ratios is just coincidental :) :p
 
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Simon F said:
No Sin and Cosine have not "been eliminated". When I did analysis at Uni', Sin and Cos were defined to be solutions to

d/dx(f(x)) = g(x)
d/dx(g(x)) = -f(x)

The fact that you can use them to measure angles and ratios is just coincidental :) :p

Heh im not sure what you were trying to get across here but im assuming you are trying to show that the derivative of sine is cosine and the derivative of cosine is -sine, which is really not stating much of anything. :p
 
mondoterrifico said:
Heh im not sure what you were trying to get across here but im assuming you are trying to show that the derivative of sine is cosine and the derivative of cosine is -sine, which is really not stating much of anything. :p
No. On the contrary, the problem, addressed in the lecture, was finding, in fact manufacturing, solutions to the differential equations:

d/dx c(x) = c(x)

and also

d/dx e(x) = f(x)
d/dx f(x) = -e(x)

The fact that the solution to the latter (apart from the trivial solution e(x)=f(x)=0) happens to be sine and cosine as commonly used to describe properties of angles was just 'interesting'.
 
I like the basic idea, but my head hurts.. :)

Basically, a rotation of a point would involve increasing the value of a spread based on an axis and solving for the coordinates I guess, sounds tricky, especially rotations around arbitrary axis. The fact that it's all algebra would be cpu friendy, maybe some future version of DirectX will include functions based on spreads or something..
 
Hmm, I doubt calculating reciprocals is better than sin or cosine from a hardware-implementation POV.
 
Simon F said:
No. On the contrary, the problem, addressed in the lecture, was finding, in fact manufacturing, solutions to the differential equations:

d/dx c(x) = c(x)

and also

d/dx e(x) = f(x)
d/dx f(x) = -e(x)

The fact that the solution to the latter (apart from the trivial solution e(x)=f(x)=0) happens to be sine and cosine as commonly used to describe properties of angles was just 'interesting'.

Heh my point was just that you putting down d/dx c(c) = c(x) (or e(x) = f(x)) is kinda meaningless. You are just saying the derivative of some function is itself. Now someone with a math background will know that you are talking about e^x, but if not you aren't giving enough information. Anyways...
 
Npl said:
Hmm, I doubt calculating reciprocals is better than sin or cosine from a hardware-implementation POV.

From my experience, reciprocals are easier in (FP) HW, but there's not a lot in it.

Given that the first chapter says that you can't add spreads directly (gosh, it sounds like mixing Vegemite and peanut butter) how does one get the equivalent of a transformation matrix?
 
mondoterrifico said:
Heh my point was just that you putting down d/dx c(c) = c(x) (or e(x) = f(x)) is kinda meaningless. You are just saying the derivative of some function is itself. Now someone with a math background will know that you are talking about e^x, but if not you aren't giving enough information. Anyways...

I can see you're going to have lots of fun when you study ODEs.

It's not meaningless at all - that'd be like saying
y = 5 x^2 + 6
y = 9 x + 20
is meaningless.

In the case I gave earlier, I had an equation (or set of equations) with unknowns and wanted to solve for those unknowns.
 
Simon F said:
No. On the contrary, the problem, addressed in the lecture, was finding, in fact manufacturing, solutions to the differential equations:

d/dx c(x) = c(x)

and also

d/dx e(x) = f(x)
d/dx f(x) = -e(x)

The fact that the solution to the latter (apart from the trivial solution e(x)=f(x)=0) happens to be sine and cosine as commonly used to describe properties of angles was just 'interesting'.

I've often found myself amazed at relations of certain things in algebraic analysis. On paper, stuff may seem really uncanny - but then, when you apply the same relations into physical world and think a little (e.g. in this case sine and cosine as points on a wheel moving at a steady velocity, and differentiation as its elementary definition leading to description of rate of change of velocity of those points), things suddenly become so obvious that you almost feel disappointment of how the equations looked pretty on the surface but mundane in their essence.

This is my (engineer's) view of mathematics, anyway.
 
Simon F said:
Given that the first chapter says that you can't add spreads directly (gosh, it sounds like mixing Vegemite and peanut butter) how does one get the equivalent of a transformation matrix?
Why would there have to be one? It's not like you use sin/cos when you actually perform the transformation.
 
MfA said:
Why would there have to be one? It's not like you use sin/cos when you actually perform the transformation.
Sorry, I meant "when setting up" the transformation.
 
It wouldnt be a lot of work to get the formulas, but what is the point? Just as normal trig doesn't give you a very good framework for working with rotations, rational trig doesn't give you a good framework for specifiying your orientation in space ... that isn't what it's meant for.
 
mondoterrifico said:
Heh im not sure what you were trying to get across here but im assuming you are trying to show that the derivative of sine is cosine and the derivative of cosine is -sine, which is really not stating much of anything. :p
I agree with Simon here, there is nothing in this world that is going to eliminate sine and cosine.

"Rational trigonometry replaces sines, cosines, tangents and a host of other trigonometric functions with elementary arithmetic. "
So what is this "rational" trigonometry? If you notice, he is still talking about trig here.

"For the past two thousand years we have relied on the false assumptions that distance is the best way to measure the separation of two points, and that angle is the best way to measure the separation of two lines."
Err... false assumptions? It is a proven fact and trig has been widely accepted and has been used since the ancient times.

"Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called "spread" and "quadrance".
What? He just probably represents trig using algebra, and goes look! I have invented another form of trig without using sine, cosine and tan methods. yeah right!

"So teachers have resigned themselves to teaching students about circles and pi and complicated trigonometric functions that relate circular arc lengths to x and y projections – all in order to analyse triangles. No wonder students are left scratching their heads,"
Scratching their heads? I dont recall scratching my head when i learnt trig. How is it complicated anyways?
 
Bahadir said:
What? He just probably represents trig using algebra, and goes look! I have invented another form of trig without using sine, cosine and tan methods. yeah right!
Just?

Personally I had never really stopped to consider that you could always give the solution to trig problems in algebraic form. Simplifying the solutions to get such a form can be a non-trivial undertaking ... yet when possible getting such solutions should always be the goal with such basic math problems, specifying solutions numerically or with transcedental functions when neither is necessary is just sloppy. With his approach it's much more straightforward, since the transcedental functions never even enter the picture.
 
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