Why?  There are two equilateral triangles.........I spread out the numbers from the MS Excel work sheet.....................................0.866025 is the distance from the origin, along the Y axis to the tip of the top equilateral triangle.........................which is the same at the bottom................the bottom half of the diamond...........the other equilateral triangle.........same exact proportions.........just upside down....................so the length of the ellipse is the just the distance from the tip of the diamond to the bottom tip of it, along the Y axis..........twice 0.866025...........................or 0.866 * 2...............which is very close to the square root of 3.............

0.5	1		0.75
0.5	0.25		0.866025
0.25	0.75
			1.732051