Geometry FAQ

We typically think of $\pi$pi, spelled "pi," as the ratio of the circumference of a circle to the diameter. The approximate value of $\pi$pi is $3.14$3, point, 14, but this irrational number has an infinite number of decimal places. $\pi$pi is important in many areas of mathematics, particularly in geometry, trigonometry, and even calculus.

Ancient Egyptians used a rough approximation of $\pi$pi to help with the construction of the pyramids. The Babylonians also had their own approximation of $\pi$pi, which is closer to the modern value than the Egyptians' estimate.

In Asia, the Chinese mathematician Liu Hui is often credited with providing one of the earliest accurate calculations of $\pi$pi. He used an inscribed hexagon to approximate the circumference of a circle, which he later refined to a $96$96-sided polygon. This allowed him to calculate $\pi$pi to five decimal places.

In India, the mathematician Aryabhata estimated $\pi$pi to four decimal places, and also provided formulas to calculate the area of a circle and the volume of a sphere.

Overall, the history of $\pi$pi is long and varied, with contributions from cultures all around the world.

Vertical angles are two angles that share a common vertex (or "corner") and are opposite each other. Complementary angles are two angles that add up to $90^\circ$90, degrees, and supplementary angles are two angles that add up to $180^\circ$180, degrees. These concepts are helpful because they mean we can measure fewer angles when creating structures and still be able to figure out the other measurements.

Try it yourself with our Finding angle measures between intersecting lines exercise.

A cross section is a "slice" of a 3D shape. For example, if we cut through a triangular prism parallel to its base, we would get a triangle-shaped cross section. On the other hand, if we cut through the same prism parallel to one of the other sides, we would get a rectangle-shaped cross section.

Understanding cross sections can help us better understand how 3D shapes are put together. Later, cross sections will help us find the volume of lots of interesting shapes, even ones with curved sides.

Try it yourself with our Cross sections of 3D objects (basic) exercise.

Scale copies and scale drawings are smaller or larger versions of a shape or object, but with the same proportions. For example, a map is a scale drawing of a geographical area. Architects often make scale drawings of buildings to help them plan out the design.

Try it yourself with our Scale copies exercise.