Math Problem ...
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Though it does not qualify as an actual mathematical proof, I've tested your approach and Jun Du's approach in Excel with 10-15 different values and I get the same results. Remember that: θ = arctan( y / x ) x = cos( θ ) y = sin( θ ) from Inverse Tangent[^] You wrote: θ = arctan((d - b) / (c - a)) x = a + (0.2*|AB|*cos(θ) y = b + (0.2*|AB|*sin(θ) and based on the link from MathWorld, (c-a) = cos( θ ) and (d-b) = sin( θ ) PJC
I just wrote it out on paper, basically if you substitute adjacent / hypotenuse in place of cos then the root will cancel out and you'll get what Jun Du gave. I'm just too exhausted from 12 hours revision plus a 2 hour shooting walk with my father and the dog. I stand corrected and apologise if I was dogmatic :-O.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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I just wrote it out on paper, basically if you substitute adjacent / hypotenuse in place of cos then the root will cancel out and you'll get what Jun Du gave. I'm just too exhausted from 12 hours revision plus a 2 hour shooting walk with my father and the dog. I stand corrected and apologise if I was dogmatic :-O.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
I stand corrected and apologise if I was dogmatic .
Hey it's cool. It happens.
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yup. he was right up until the last little bit of arithmetic. Cleek | Image Toolkits | Thumbnail maker
Chris Losinger wrote:
he was right up until the last little bit of arithmetic.
I had that happen when I was in Calculus 15 years ago. It happens. The teacher dinged everyone on arithmetic mistakes even if we displayed knowledge of the material. Now I look back at those old midterm exams and laugh. PJC
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I just wrote it out on paper, basically if you substitute adjacent / hypotenuse in place of cos then the root will cancel out and you'll get what Jun Du gave. I'm just too exhausted from 12 hours revision plus a 2 hour shooting walk with my father and the dog. I stand corrected and apologise if I was dogmatic :-O.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
happens to the best of us... and the least :) without sitting down and working it through, i don't see how DU's solution works. maybe i'll give it some time later tonight. Cleek | Image Toolkits | Thumbnail maker
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happens to the best of us... and the least :) without sitting down and working it through, i don't see how DU's solution works. maybe i'll give it some time later tonight. Cleek | Image Toolkits | Thumbnail maker
When substituting cos θ by
x2 - x1
√(y2 - y1)² + (x2 - x1)²
the magnitude of the two vectors cancel out and you are left with
x2 - x1With the equation for the y component, sin θ is substituted by
y2 - y1
√(y2 - y1)² + (x2 - x1)²
the magnitude of the two vectors cancelled out again and you are left with
y2 - y1So in Jun Du's method, the magnitude of the two vectors and the trig functions drop out. PJC
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I just wrote it out on paper, basically if you substitute adjacent / hypotenuse in place of cos then the root will cancel out and you'll get what Jun Du gave. I'm just too exhausted from 12 hours revision plus a 2 hour shooting walk with my father and the dog. I stand corrected and apologise if I was dogmatic :-O.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
As a friendly suggestion, I would recommend bookmarking the www.mathworld.com[^] link. I use it often as a good web reference :) Paul
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Hey Guys, I have a math issue, I know how you like brain teasers so I thought I would post it here, say I have two points ab & cd, how do I find the point 20% of distance between these two points on the same slope ? Regards Ray "Je Suis Mort De Rire" Blogging @ Keratoconus Watch
here it is suppose a and b are points.. I want point C 20% from point a then c.x= a.x+ 0.2 * (distnce between a & b ) * cos (angle between a and b ); c.Y= a.y+ 0.2 * (distnce between a & b ) * sin (angle between a and b ); Leya -- modified at 3:04 Wednesday 14th June, 2006
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Hey Guys, I have a math issue, I know how you like brain teasers so I thought I would post it here, say I have two points ab & cd, how do I find the point 20% of distance between these two points on the same slope ? Regards Ray "Je Suis Mort De Rire" Blogging @ Keratoconus Watch
Use a tape measure :) I still remember having to write your own code in FORTRAN rather than be a cut and paste merchant being pampered by colour coded Intellisense - ahh proper programming - those were the days :)
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As a friendly suggestion, I would recommend bookmarking the www.mathworld.com[^] link. I use it often as a good web reference :) Paul
I know about MathWorld since I've got a copy of Mathematica, it's just I was being blind to the obvious yesterday, was feeling a bit more awake today but then sat down outside to read a book in the sun, big mistake.. Fell alseep.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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happens to the best of us... and the least :) without sitting down and working it through, i don't see how DU's solution works. maybe i'll give it some time later tonight. Cleek | Image Toolkits | Thumbnail maker
Chris Losinger wrote:
happens to the best of us
God I hope you're not implying I'm one of the best :laugh: Far from it.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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Use a tape measure :) I still remember having to write your own code in FORTRAN rather than be a cut and paste merchant being pampered by colour coded Intellisense - ahh proper programming - those were the days :)
I was told I was making things too complicated (which I was by the way), I think you're oversimplifying a bit here :laugh: But it's the most realiable method, I've got to give you that.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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I know about MathWorld since I've got a copy of Mathematica, it's just I was being blind to the obvious yesterday, was feeling a bit more awake today but then sat down outside to read a book in the sun, big mistake.. Fell alseep.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
Mathematica
I've always liked mathematica. Haven't worked with it in some time :sigh:
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Ed.Poore wrote:
Mathematica
I've always liked mathematica. Haven't worked with it in some time :sigh:
Havn't used it much but liked what I saw, but I find it's more fun to program your own stuff rather than getting Mathematica to do it. Mind you, you do get a sense of satisfaction when asking it to calculate Pi to 5,000,000 places, you think it's crashed and then you go off to supper, lo and behold when you come back it's done it.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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Hey Guys, I have a math issue, I know how you like brain teasers so I thought I would post it here, say I have two points ab & cd, how do I find the point 20% of distance between these two points on the same slope ? Regards Ray "Je Suis Mort De Rire" Blogging @ Keratoconus Watch
Ray Kinsella wrote:
I have a math issue, I know how you like brain teasers so I thought I would post it here, say I have two points ab & cd, how do I find the point 20% of distance between these two points on the same slope ?
Ask an Asian? Michael Martin Australia "I controlled my laughter and simple said "No,I am very busy,so I can't write any code for you". The moment they heard this all the smiling face turned into a sad looking face and one of them farted. So I had to leave the place as soon as possible." - Mr.Prakash 24/04/2004
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Havn't used it much but liked what I saw, but I find it's more fun to program your own stuff rather than getting Mathematica to do it. Mind you, you do get a sense of satisfaction when asking it to calculate Pi to 5,000,000 places, you think it's crashed and then you go off to supper, lo and behold when you come back it's done it.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
it's more fun to program your own stuff rather than getting Mathematica to do it
I agree. It's nice to use a tool like Mathematica to check the program to ensure it is working correctly :) Took a Graduate course called Super Visualization and tools like Mathematica and SciLab were quite useful.
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Ed.Poore wrote:
it's more fun to program your own stuff rather than getting Mathematica to do it
I agree. It's nice to use a tool like Mathematica to check the program to ensure it is working correctly :) Took a Graduate course called Super Visualization and tools like Mathematica and SciLab were quite useful.
What's your opinion of SciLab?
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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What's your opinion of SciLab?
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
What's your opinion of SciLab?
It is pretty alright. Had to use it in conjunction with MuPad to solve a problem with wavelet transforms. PJC
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Ed.Poore wrote:
What's your opinion of SciLab?
It is pretty alright. Had to use it in conjunction with MuPad to solve a problem with wavelet transforms. PJC
:nod politely and pretend to understand: :-D
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
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:nod politely and pretend to understand: :-D
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
:nod politely and pretend to understand:
:laugh::laugh::laugh: When I look at my old take-home final exam for that Super Visualization course, I still scratch my head over the wavelet transforms stuff :-D
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Jun Du wrote:
This is a perfect example that how people make things more complicated than they should be
Maybe it's more complicated but it works. Here's the proof using simple Pythagorean trig and his theorem.
Start with a 3,4,5 triangle with height 3 and width 4 (and hypotenuse 5).
If A is the bottom left-corner, located over an "origin" of (0,0) then it follows that
A = (0,0) (bottom-left corner)
B = (4,3) (top-right corner)
C = (4,0) (bottom-right corner)
θ = Angle BAC (i.e. bottom-left)
Also it can be shown (through Pythagorean Trigonometry) that:
sin(θ)=3/5
cos(θ)=4/5
tan(θ)=3/4So you require 20% of the line AB (in this case it is (0.2*5) = 1).
We can let the co-ordinates of the end point of this line (from A along AB for 20% of AB) be X=(x,y).
It then follows that since we have a hypotenuse equal to 1 and the angle has remained the same that:x = 1*cos(θ) = 4/5
y = 1*sin(θ) = 3/5So from A the new point X which is 20% of the line AB is A+X, i.e: X = (0 + 4/5, 0 + 3/5) = (4/5, 3/5).
If you take you're equations of:
x = a + 0.2 * (c - a)
y = b + 0.2 * (d - b)
You will get the following answers for this case:
x = 0 + 0.2 * (4 - 0) = 0.2 * 2 = 2/5
y = 0 + 0.2 * (3 - 0) = 0.2 * 3 = 9/10
Which is not the same as the ones above.The simplest proof that the previous equations are wrong can be shown quite simply by Pythagoras' Theorem.
If we assume that the triangle formed is of height and width 1 then, your equations show that the height and width of the "new" triangle which provides 20% of AB are both 0.2.
If you use Pythagoras on these you get a hypotenuse of √(0.2²+0.2²) which gives √0.08 which is ~0.2828, not 0.2 as you require.
Formula 1 - Short for "F1 Racing" - named after the standard "help" key in Windows, it's a sport where participants desperately search through software help files trying to find actual documentation. It's tedious and somewhat cruel, most matches ending in a draw as no participant is able to find anything helpful. - Shog9
Ed.Poore wrote:
x = 1*cos(θ) = 4/5 y = 1*sin(θ) = 3/5
This is wrong. The length of hypotenuse is 5, not 1.
Ed.Poore wrote:
x = 0 + 0.2 * (4 - 0) = 0.2 * 2 = 2/5 y = 0 + 0.2 * (3 - 0) = 0.2 * 3 = 9/10
This is wrong. How come 4-0 becomes 2, 0.2*3 becomes 9/10? If you hadn't made these mistakes, you could have just proved my formulas, but in a complicated way. - It's easier to make than to correct a mistake.