## Facts

Hey, did you know?

A pentagon is a five-sided, simple polygon. A simple polygon doesn’t intersect itself and resembles a star.

The word “pentagon” has Greek roots, meaning five angles.

The most famous pentagon is also one of the world’s largest office buildings. Located in Arlington Va., near Washington D.C., The Pentagon is a facility that’s nearly 30 acres and home to the U.S. Department of Defense.

In geometry, a pyramid is defined as a polyhedron made by connecting a polygonal base (a 2D shape with three or more straight sides) with a point at the top, called the apex. The base of a pyramid can be a triangle, a square, or a rectangle. Each side of a pyramid (each base edge and the apex) forms a triangle. The shape of a pyramid allows weight to be distributed evenly throughout the structure. Most of the weight in a pyramid is on the bottom and it decreases the higher you go. This allowed ancient civilizations to create huge structures of stone that were very sturdy.

Deep in the rainforests of Guatemala is Tikal. More than 3,000 structures—mostly pyramids—remain from the ancient Mayan city, Yax Mutal. It was once the capital of one of the most powerful kingdoms of an ancient empire, dating to the fourth century B.C.

Pyramids are not just in ancient Egypt. The Louvre Pyramid in Paris is a modern glass structure that serves as the main entrance to the Louvre Museum. Created by architect I.M. Pei, it opened in 1989.

A prism provides an instant rainbow. A prism is a pyramid-shaped object usually made of transparent glass or plastic. Matter that’s transparent allows light to pass through it. A prism transmits light but slows it down. When light passes from air to the glass of the prism, the change in speed causes the light to change direction and bend. With the differences in the refraction index between the air and the glass, the light bends once entering the prism to make a rainbow.

Soap bubbles have very thin walls. The range can be anywhere from 10 nanometers at the top of a thin-walled bubble to over 1000 nanometers. By contrast, human hair's thickness range is on the order of 40,000 to 60,000 nanometers.”

## Geography

Let’s take a world tour! Get your passport ready!

Cornwall, UK

Living in a bubble

The Eden Project is currently home to the world’s largest greenhouse and it resembles a blob of freshly blown bubbles. Located in Cornwall, England, it’s composed of geodesic domes made up of hexagonal and pentagonal cells. The Eden Project focuses on green living and that was considered that in every aspect of the design and programming of the structure. The interactive education center known as “The Core” incorporated Fibonacci numbers (a math sequence that relates to the branching, flowering, or arrangement of things in nature) and phyllotaxis (the arrangement of leaves) in its design.

Rotterdam, The Netherlands

Go Clean Your Cube!

The Cube Houses in Rotterdam, the Netherlands, are one of the city’s most iconic attractions. Designed by Dutch architect Piet Blom in the late 1970s, these homes are literally cubes, tilted over by 45 degrees. The Cube Houses were designed asymmetrically to resemble an abstract forest, each triangular roof representing a treetop.

Constructed on concrete pillars with wooden framing, each one stands three-floors tall. The ground floor is the entrance, the first floor contains an open kitchen and living room, the second floor houses a bathroom and two bedrooms. In some cases, the top floor is a rooftop garden. Step inside and you’ll see that the walls are slanted.

It’s a Right Triangle: The Flatiron Building

In the early 1900s, the construction of New York City’s Flatiron Building inspired skepticism about whether its triangle steel frame was stable enough to stand when completed. Shaped like a perfect right triangle, the building measures only six feet across the narrow end.

Flatiron District, New York, United States

Segovia, Spain

Engineering Marvels: Roman Aqueducts

First developed around 312 B.C., aqueducts use gravity to transport water along pipelines into city centers. The Romans didn’t invent the aqueduct—primitive canals for irrigation and water transport existed earlier in Egypt, Assyria, and Babylon. But the Romans used their mastery of civil engineering to perfect the process. Hundreds of aqueducts eventually sprang up throughout the empire, transporting water as far as 60 miles. Roman aqueducts were so well built that some are still in use today. Rome’s famous Trevi Fountain is supplied by a restored version of the Aqua Virgo, one of ancient Rome’s 11 aqueducts.

Roma, Italy

Why the Parthenon is an Optical Illusion

Completed in 432 B.C., the Parthenon in Greece was a temple to the goddess Athena. The Parthenon appears perfectly straight and symmetrical. But, in reality, its subtly curved, beginning at its foundation and running up through the roof. This was done deliberately using techniques angling the blocks of the steps, tilting the columns slightly inward, and making the corner columns slightly thicker than the others.

These optical refinements serve as a sort of “reverse optical illusion.” The Greeks may have realized that two parallel lines appear to bow, or curve outward, when intersected by converging lines. In this case, the ceiling and floor of the temple may seem to bow in the presence of the surrounding angles of the building. Striving for perfection, the designers may have added curves allowing the temple to be seen as they intended—perfectly straight.

There’s a Hole in the Pantheon’s Ceiling

The Pantheon in Rome was first built as a temple to all gods, completed in 125 A.D. The most fascinating part of the Pantheon is its giant dome, with a hole (oculus) at the top. The dome was the largest in the world for 1,300 years and currently remains the largest unsupported dome in the world. The diameter of the dome is 142 feet (the U.S. Capitol dome is 96 feet) and it’s in perfect proportion with the Pantheon—the distance from the floor to the top of the dome is exactly equal to its diameter.

Roman engineers lightened the dome’s massive weight as much as possible. As they decreased thickness, it created the effect that while the interior of the ceiling is spherical, its exterior is slightly “flattened”. The oculus is 27 feet in diameter and is the only source of light. Rain occasionally falls through it, but the floor is slanted and drains the water.

Via del Pantheon, Roma, Italy

## History

When Einstein Calls You a Genius

German-born Emmy Noether (1882-1935) is arguably the most influential female mathematician in history. Noether is best known for discovering Noether’s Theorem, which links mathematics and physics in an extremely important way. The theorem, which is named after her, relates the laws of nature and conservation to mathematical symmetry and how we understand the universe.

At the time, her theory was truly groundbreaking and influenced how mathematicians and scientists understood the workings of our universe. She also made major contributions to the fields of theoretical physics and abstract algebra.

She was so smart that Albert Einstein said Noether is, “the most significant mathematical genius thus far produced since the higher education of women began.

Math Dad: Archimedes

In the third century B.C., Archimedes, known as the father of mathematics, discovered the law of hydrostatics. It states that a body immersed in fluid loses weight equal to the weight of the amount of fluid it displaces. He also discovered the laws of levers and pulleys, allowing us to move heavy objects using small forces.

Outta This World!

Mae Carol Jemison (1956-present) is a decorated engineer, physician, mathematician, and NASA astronaut. She’s the first African American woman to go to outer space. Jemison was a member of the Endeavour Space Shuttle that launched into orbit in 1992. She now serves on the council for the Science Matters initiative, with the goal of encouraging children to pursue STEM careers.

World’s First Female Math Teacher

Hypatia, (370-415 A.D.), was the daughter of a prominent, upper-class Egyptian mathematician and philosopher, named Theon. This allowed her to receive the same education as the boys. But she quickly became a more accomplished mathematician than anyone, including her father. It was an accomplishment that was unusual for a woman in Egypt. She is considered the first known female math teacher in history. Hypatia also made several advancements to the field of mathematics, namely her work on conic sections and developing the concepts of ellipses, parabolas, and ellipses by dividing cones into planes.

Ancient Math Homework

The Tang Dynasty in China (618-907 A.D.) is considered a high point in Chinese civilization and a golden age of cosmopolitan culture, according to historians. During this time, the study of math was standard in schools. The Ten Computational Canons was a collection of 10 Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng. It was the official text for imperial examinations in mathematics.

## Pop Your Favorite Joke

What’s a bubbles’ favorite type of music?

Pop music.

How do mathematicians commute to work?

They take the rhombus.

What did the triangle say to the circle?

You're pointless.

Where do geometry teachers post selfies?

On Parallelogram

Why couldn’t the scientist make bubbles?

He couldn’t find the right solution.

What did the geometry teacher say when his parrot went missing?

Polygon

What did the 90° angle say after an argument?

It turns out, I was right.

Why is the obtuse triangle always upset?

Because he’s never right.

Why couldn’t the polygon play in the big game?

He hurt his quadrilateral.

## Pop Your Favorite Joke

What’s a bubbles’ favorite type of music?

Pop music.

How do mathematicians commute to work?

They take the rhombus.

What did the triangle say to the circle?

You're pointless.

Where do geometry teachers post selfies?

On Parallelogram

Why couldn’t the scientist make bubbles?

He couldn’t find the right solution.

What did the geometry teacher say when his parrot went missing?

Polygon

What did the 90° angle say after an argument?

It turns out, I was right.

Why is the obtuse triangle always upset?

Because he’s never right.

Why couldn’t the polygon play in the big game?

He hurt his quadrilateral.