# Thread: Transforming a unit square into a parallelogram

1. Unit Square A.jpg

Unit Square B.jpg

Goal: To transform a unit square into a parallelogram in which (a) the diagonals are parallel to the unit square's diagonals, (b) the longest diagonal is equal in length to either of the unit square's diagonals, and (c) the diagonals intersect at the midpoint of the longest diagonal.

Using basic algebra, not trigonometry or matrix format, what is/are the transformation equation(s)?

2. What does that rhombus inscribed in your second square have to do with your written description?

3. Originally Posted by pikpobedy
What does that rhombus inscribed in your second square have to do with your written description?
"
Parallelogram - Wikipedia, the free encyclopedia says: "a parallelogram is a simple (non self-intersecting) quadrilateral with two pairs of parallel sides" and "Rhombus – A parallelogram with four sides of equal length."

http://http://en.wikipedia.org/wiki/Rhombus says: "a rhombus ... is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length" and "Every rhombus is a parallelogram, and a rhombus with right angles is a square."

So, technically, I suppose, my second figure is of a rhombus inscribed in a rhombus.

In answer to your question, "the rhombus inscribed in the square" is the parallelogram into which "the second square" is to be transformed.

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