Square and equilateral triangle problem

[#cruncher]

I am trying to find where equilateral triangles stacked end to end equal a whole number (to match with squares).
My trig is rusty to say the least but an equilateral triangle with sides of 1 has a middle of .86602ish 0.5^2 + x^2 = 1^2


How would I find x * .86602= lowest whole number

I appreciate your time and any help.

 

[lev888]

I am trying to find where equilateral triangles stacked end to end equal a whole number

What equals whole number?

 

[lookagain]

I am trying to find where equilateral triangles stacked end to end equal a whole number (to match with squares).
My trig is rusty to say the least but an equilateral triangle with sides of 1 has a middle of .86602ish 0.5^2 + x^2 = 1^2


How would I find x * .86602= lowest whole number

I appreciate your time and any help.

 

[lookagain]

#cruncher, the height of the equilateral triangles is half of the square root
of three. It is irrational. No positive multiples of it will give an integer. So,
if you keep stacking the triangles and the squares, none of the tops of the
triangles will ever line up with the tops of the squares.

 

[lev888]

I am trying to find where equilateral triangles stacked end to end equal a whole number (to match with squares).

Is this a math problem or it's related to something like tiling or woodworking? In other words, how equal do you want your equal to be?

 

[#cruncher]

Sorry, hard to articulate my question. Stacking squares will increase 1 + 1 + 1.... Stacking the triangles will increase .86602 + .86602 + .86602....
You stack 10,000 triangles and it would match 86602 stacked squares. I wanted to figure out if there was sum distance covered of the stacked triangles that was a whole number lower than 86602.

Thanks again all!

 

[#cruncher]

If I rounded to .87, it would be 100 triangles to 87 squares. Doubt there is a lower whole number than that. Oh well, thanks for the responses everyone.

 

[lev888]

Sorry, hard to articulate my question. Stacking squares will increase 1 + 1 + 1.... Stacking the triangles will increase .86602 + .86602 + .86602....
You stack 10,000 triangles and it would match 86602 stacked squares. I wanted to figure out if there was sum distance covered of the stacked triangles that was a whole number lower than 86602.

Thanks again all!

10,000 is not enough. 100,000 gets you 86602. Since it's even, we can divide both by 2, therefore 50,000 gets you 43301.