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Extra resources for A treatise on the analytical geometry of the point, line, circle, and conical sections (1885)
12. Create one mandala that uses techniques from Islamic art, is a knot design, and also has optical effects. ” Hindus use mandala designs for meditation. The Indian rug at right is an example of a mandala, as is the Aztec calendar stone below left. Notice the symbols are arranged symmetrically within each circle. The rose windows in many gothic cathedrals, like the one below right from the Chartres Cathedral in France, are also mandalas. Notice all the circles within circles, each one filled with a design or picture.
26. Find possible coordinates of a point Q so that QR || TS. 27. A partial mirror reflects some light and lets the rest of the light pass through. In the figure at right, half the light from point A passes through the partial mirror to point B. Copy the figure, then draw the outgoing angle for the light reflected from the mirror. What do you notice about the ray of reflected light and the ray of light that passes through?
Notice that the floor plans of the towers have the shape of Islamic designs. Use your compass and straightedge to re-create the design of the base of the Petronas Twin Towers, shown at right. 6. Use your protractor and ruler to draw a square tile. Use your compass, straightedge, and eraser to modify and decorate it. See the example in this lesson for ideas, but yours can be different. Be creative! 7. Construct a regular hexagon tile and modify and decorate it. See the example in this lesson for ideas, but yours can be different.