Arches and designs

The constructions so far were tools. Now use them to draw real shapes — the arches you can see in buildings.

A Trefoil Arch appears in Central Park in New York and in the Diwan-i-Aam at the Red Fort. How were such arches made? The first step is always to be able to draw them exactly on a flat surface, whether paper or stone.

And the way to draw one exactly is to plan the support lines first — the lines that hold the figure's proportions but do not appear in the finished drawing, exactly like the line XY in the eye construction.

For a trefoil arch to be symmetrical, we need AB = CD and ∠BAD = ∠CDA. You now know how to get both: equal lengths with a compass, and equal angles by copying an angle.

So: construct equal angles at A and at D, mark B and C such that AB = CD, and you have the support lines. Then draw the arcs on them. If the arch does not look right, adjust the radii of the arcs — the support lines fix the symmetry, and the radii are free for you to choose by eye.

A pointed arch, like another at the Diwan-i-Aam, needs even less. Its support lines are just two line segments of equal length. Mark their midpoints, and you can construct the arch — this is the same idea as 'Wavy Wave' from the Grade 6 textbook.

Change the radius of the arcs and you get different arches from the same support lines. That is how a designer works: the construction guarantees the symmetry, and the choices left over are where the style comes from. Make your own arch designs this way.