Question

Is it possible to find lattice points that are (sqrt of 15) units apart?

Answer 1

I don't see why not. root-15 is irrational, so you might be limited depending on the situation.

Answer 2

Hint: Graph the circle x^2 + y^2 = 15

Answer 3

what is the definition of a lattice point? Are there restrictions?

Answer 4

No restrictions. A lattice point is a point whose coordinates are integers.

Answer 5

Did you graph x^2+y^2 = 15?

Answer 6

I'm not sure how to do that.

Answer 7

if you have to be integer, then I don't see how

Answer 8

It's the circle with center (0,0) and it has a radius of sqrt(15)

Either use a graphing calculator or wolfram alpha to help

Answer 9

take a sheet of graph paper, and define the units as sqrt(15) ..

Answer 10

I assume by definition, all distances are measured in units of "distance between adjacent lattice points"

Answer 11

I'm not sure I can use the circle....we've only really learned about using this with the Pythagorean theorem....

Answer 12

The equation for a circle *is* the Pythagorean theorem!

Answer 13

And, that's not how i completed the first question. The first question asked me to find two points that were (square-root of 13) units away. And I found those points, however, it also asked if it was possible to get lattice (whole integer) points that were exactly (square-root of 15) units apart. All I want to know is if it's possible with whole numbers...

Answer 14

I would answer this way:
lattice points are an integer distance apart on the x axis, or on the y axis
if you had 2 units apart on the x and 3 units on the y, then (on the diagonal) you could get a pair that is sqrt(2^2 + 3^2)= sqrt(13) apart.
but if you look at all pairs for 15, you will not get a pair which are perfect squares