Make your own arch designs.

Question

Homi · Accepted Answer

Arches are strong curved structures. We can design them using simple geometric shapes.

Step 1 — Semicircular Arch

This arch is shaped like half a circle. It is a very common arch design.

Let us choose the width of our arch. We call this the span. Let the span be 8 units. The radius of the semicircle is half of the span.

Let us calculate the radius. $\text{Radius} = \frac{\text{Span}}{2}$

$= \frac{8}{2}$

$\boxed{\textbf{4 units}}$

The center of the circle is at the midpoint of the span. We draw a semicircle.

Diagram 1

Step 2 — Pointed Arch

This arch has two curved sides. They meet at a point at the top. This is also called a Gothic arch.

Let us choose the width of our arch. Let the span be 8 units. Each curved side has a radius. This radius is equal to the span.

Let us state the radius for each arc. $\text{Radius} = \text{Span}$

$= \textbf{8 units}$

$\boxed{\textbf{8 units}}$

The centers of the arcs are at the ends of the span. We draw two arcs. They meet at the top.

Diagram 2

Step 3 — Segmental Arch

This arch is a part of a circle. It is flatter than a semicircle.

Let us choose a radius for our arch. Let the radius be 5 units. Let us choose the center of the circle. It is below the span. Let the center be 3 units below the span's midpoint.

We can find the span using Pythagoras theorem. Let half of the span be $x$ . The radius is the hypotenuse of a right triangle. The vertical distance is 3 units. The horizontal distance is $x$ .

$x^2 + 3^2 = 5^2$

$x^2 + 9 = 25$

$x^2 = 25 - 9$

$x^2 = 16$

$x = \sqrt{16}$

$x = \textbf{4 units}$

The total span is twice this value. $\text{Total Span} = 2 \times x$

$= 2 \times 4$

$\boxed{\textbf{8 units}}$

We draw an arc using this center and radius.

Diagram 3

Answer

(i) Semicircular Arch: A simple arch, half a circle. (ii) Pointed Arch: Two arcs meeting at a point. (iii) Segmental Arch: A flatter arch, part of a circle.

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