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#1 2006-05-26 03:45:10

mikau
Member
Registered: 2005-08-22
Posts: 1,504

logarithmic coordinates

I picked up a physics book at my local library, it begins with a review of what appears to be precalc level mathematics. I already know pretty much everything but they mentioned a few nifty things I've not heard of. Particularly logarithmic coordinates. The book has a wierd habit of stating restrictions on the domain and range that do not exist. For instance the book had an xy plane where the coordinate only go from -1 to 1 across the page, the book had the stipulation -1 <= x <= 1, the drawing was within those boundaries but I could see no reason why the independant variable could not have a greater absolute value then 1.

I just want to see if I got it straight,

the independant x coordinates are evenly spaced, the y coordinate is an exponant of a given base a, so to find the return value of a function at a given x coordinate by a^y.

So I suppose if it were graphed in base e, the graph of y = e^x would be a straight line that would look just like the standard graph of y = x.

I suppose also the function and or domain must be restricted such that f(x) > 0 or the logarithmic coordinates won't work.

The book gave a lousy explanation so I'm just trying to make sure I've got it right.

Last edited by mikau (2006-05-26 03:49:21)


A logarithm is just a misspelled algorithm.

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#2 2006-05-26 09:02:11

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: logarithmic coordinates

You got it.  Logarithmic coordinates are generally used when you want to show a graph of data where both very small values and very large are significant.  It's the best way to see both worlds on the same graph.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-05-26 12:39:50

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,534

Re: logarithmic coordinates

Yep, those graphs that crawl along the x axis then shoot right up at the end are pretty useless - they all look alike. But put them on a log graph and you can see hidden details.

I should make one for the website ... one day ... when there is time ...


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-05-26 12:51:41

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: logarithmic coordinates

very sweet. Too bad its restricted to positive numers...


A logarithm is just a misspelled algorithm.

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#5 2006-05-26 16:30:57

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: logarithmic coordinates

It's not exactly restricted to positive number.  Just plot a y axis where the first tick mark is -e, the second is -e^2, the third is -e^3, and so on.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-05-27 04:59:09

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: logarithmic coordinates

yeah but both can't be done at once. :-/


A logarithm is just a misspelled algorithm.

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#7 2006-05-27 14:24:22

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: logarithmic coordinates

Think the y axis to be fake, it displays some loga10 loga5 instead of 10 and 5, so same distance means multiplied by same value.


X'(y-Xβ)=0

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