Convert the area of a circle into an rectangle shaped area of the same size. This example demonstrates how to construct the golden rectangle using a compass and ruler. Specify pos as a four-element vector of the form [x y w h] in data units. The quantity we need to maximize is the area of the rectangle which is given by .

We want to construct a square with same area. Specify values between 0 (no curvature) and 1 (maximum curvature). The golden rectangle is a rectangle whose sides form the golden ratio which is a naturally occurring number approximately equal to . Steps.

Construct a circle centered at M with radius OA. Fig. rectangle('Position',pos,'Curvature',cur) adds curvature to the sides of the rectangle. Construct a square inscribed inside the circle. 10.1.
rectangle('Position',pos) creates a rectangle in 2-D coordinates. Complete by constructing a square with side BF. 1 Two-circle method. There are only two cases when the circle intersects with the rectangle: Either the circle's centre lies inside the rectangle, or; One of the edges of the rectangle has a point in the circle. In other words, you're making a new Rectangle whose name is box. Construct two concentric circles equal in diameter to the major and minor axes of the required ellipse. Let F be the point where the circle and ray CB intersect. The function plots into the current axes …


Extend side CB. Note! Then BF is the side of the desired square. 10.1 Two-circle construction for an ellipse. Then construct a circle with center at point and radius . Creating a Golden Rectangle is pretty straightforward, and starts with a basic square. - The algorithm is quite simple - switching rectangle width and height may influence the number calculated.Switching the input values above changes the layout and gives . Always use a pencil in case you need to go back and re-work any of your drawn shapes. Works much the same way as a circle to square conversion but you will have to enter the width of the rectangle in addition to the circle's diameter.

And we also have to remember that the two diagonals of the square are going to be perpendicular bisectors of each other. 2 circles and a rectangle For different curvatures along the horizontal and vertical sides, specify cur as a two-element vector of the form [horizontal vertical].For the same length of curvature along all sides, specify cur as a scalar value. We note that the radius of the circle is constant and that all parameters of the inscribed rectangle are variable. A drawing compass allows you to attach a writing tool on the mobile point of the compass. Let’s say the rectangle is x by y, so the area is x * y. For the square to be the same area, the side of the square would have to be of length [square root of (x * y)]. A = wh. Follow the steps below to create your own Golden Ratio:


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