Chapter 12 Project: Going in Circles.
Activity 1: Doing.
This knot is made using a graph paper and a compass.
The circles were drawn with centers (0,5), (5,0), (0, -5), (-5,0), and with an outer radius of 5√2. The inner circles’ radius was 4√2. The four centers were then connected to form a square. Segments were drawn through intersections of larger and smaller circles.
Activity 2: Exploring.
Figure A has three circles inscribed in the outer/ main circle. Both figure A and B circles are drawn to the same scale. Figure B is an altered orientation of A, with equal sections if the main circle shifted at a particular linear scale factor and made to intersect with the subsequent circles towards the center. This alteration is what gives figure B a new look. Much as figures A and B are congruent, the modification in sections of the circles makes B to form a spectrum. When the two-dimensional face of B is rotated at a first speed, then it would create an expression of A, which is the original drawing.
In my design, I transformed squares that were inscribed in one main square to form a flower pattern. The squares are inclined at an angle as they decrease in size with a constant area scale factor. From a point, the lines touch the opposite side of the squares at an angle. This is repeated several to form a flowery pattern that appears as if four circles were used to bisect the square into four equal parts.
Activity 3: Constructing.
In this construction, a circle was drawn and two squares that were rotated at 45 0 inscribed in it. A second circle was then inscribed in the squares. Diagonal lines were then drawn in each square. The central angles of the smaller circle were then bisected. Two circles were then inscribed and painted to make the design.
Finishing the project.
This design will be used to make a tile pattern for a floor. The purpose of this design, therefore, is to develop a unique pattern that will be scripted on tiles. In drawing this design, the outer square was drawn, and then other rotated squares inscribed in it. These inscribed squares were rotated at 50 and reduced at a constant area scale factor towards the center. The geometric concepts incorporated in this design included rotations, reduction of the area scale factor, and inscribing.