Golden Section Rectangle

The golden rectangle s sides have a special relationship.

Golden section rectangle. Let us pick the side ab and call its mid point as. Connect the mid point p to a corner of the opposite side. The golden rectangle is a rectangle whose sides are in the golden ratio that is a b a a b where a is the width and a b is the length of the rectangle.

Draw a line from the midpoint of one side of the square to an opposite corner. A golden rectangle with longer side a and shorter side b when placed adjacent to a square with sides of length a will produce a similar golden rectangle with longer side a b and shorter side a. The ratio calculator is an effective tool to assist in calculating ratios in general while the golden ratio calculator will do the same as the golden rectangle calculator with the exception of finding the area of the rectangle.

Let us name the vertices of the square as a b c and d. φ 1 2 5 2 the square root of 5 is approximately 2 236068 so the golden ratio is approximately 0 5 2 236068 2 1 618034. This is a rectangle where if you cut off a square side length equal to the shortest side of the rectangle the rectangle that s left will have the same proportions as the original rectangle.

The golden rectangle is a rectangle with a length of a band width of a. Since p lies on the side ab the. If a golden rectangle with a longer side a and a shorter side b is placed next to a square with sides measuring a then a b a a b.

This illustrates the relationship a b a a b φ displaystyle frac a b a frac a b equiv varphi. When people think of shapes with golden section ratios they typically think of a golden rectangle where one side divided by the other is 1 618. However a variety of mathematics can be applied to different layouts and a variety of shapes can be constructed from golden section proportions.

This rectangle is often seen in art as it has been said it s the most pleasing to the eye of all such rectangles. A proportion such as one involving a line divided into two segments or the length and width of a rectangle and their sum in which the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller. The golden rectangle calculator is a convenient way to find the golden rectangle instead of working it by hand.