Floor function

[Luma]

Hi Lime, I'm sorry that I didn't follow up, it's not that I dawdled but my laptop was giving me a hard time

Back to the problem. I'm not sure that I can sketch x² - [x²] properly, specially when I first sketched [x²], I made approximations.

My question is: Is it correct to equate f(x) and g(x) and find the x then say for the values that satisfies x there's a solution?

[lime]

You can find the solution here only by trying to imagine the graphs and their intersections.

[Luma]

Originally Posted by lime

You can find the solution here only by trying to imagine the graphs and their intersections.

Well, I sketch f(x) = x² - floor(x²) and g(x) = (x - floor(x))² using Excel on the interval [1,2]. I made approximations, I mean I took values for x: 1.01. 1.02, ..., 1.99,2. Take a look at the graph:
http://img27.imageshack.us/img27/6518/20254863.jpg

Is my graph correct? Does that mean we have a solution on the intersection points?

[lime]

Besides vertical blue lines and scale on the x-axis, this seems pretty close to the truth.

[Luma]

Originally Posted by lime

Besides vertical blue lines and scale on the x-axis, this seems pretty close to the truth.

I stretched the x-axis, but I can't help with the vertical blue lines because at the end this an approximation, if x values were preciser , the lines would look more accurate.

http://img44.imageshack.us/img44/1420/73138143.jpg

[lime]

Hint!

Plot[{x^2 - Floor[x^2], FractionalPart[x]^2}, {x, 0, 4}, 
 PlotRange -> {0, 1.5}]

in Mathematica gives http://img136.imageshack.us/img136/584/plot.gif.

[Luma]

Originally Posted by lime

Hint!

Plot[{x^2 - Floor[x^2], FractionalPart[x]^2}, {x, 0, 4}, 
 PlotRange -> {0, 1.5}]

in Mathematica gives http://img136.imageshack.us/img136/584/plot.gif.

Actually I was looking for the Matlab setup files (I used to have it) but I couldn't find it ... that's why I used Excel at the end

well ... after 25 replies we reached the answer, not bad I guess, next time I'll think twice before I mess up with math posts

[lime]

Did we reach the answer??? I think we didn't, did we?!?

[Luma]

Originally Posted by lime

Did we reach the answer??? I think we didn't, did we?!?

at least I had my answer for interval [1,2].

[lime]

at least I had my answer for interval [1,2].

What it was?