One member of the Buzzmath team recently visited Chicago, IL, and noticed how much the Windy City resembles mysterious Buzzcity. Just like the chaotic and disordered place that has become Buzzcity, it seems that the architecture of every building in Chicago was carefully created from a mathematical point of view.

Furthermore, Chicago was destroyed by a terrible fire in 1871. Like Buzzcity, it had to rely on experts to reconstruct. Those experts were brilliant architects who used a revolutionary technology (back then) that allowed them to push further the limits of height: steel frames.

We spotted many skyscrapers and other buildings using well-known notions of mathematics, geometry for the most part.

Triangular prisms

When you think about it, all buildings are built on a prism base, generally rectangular. However, Chicago is full of triangular buildings, like this one:

This one is the 200 South Wacker Drive, an office building that was built from two triangular prisms joined together at hypotenuse.

Only in Chicago can you find such a stylish correctional center (from an outside point of view, of course)!

Harry Weese, the architect that imagined the correctional center above, was a triangle passionate, we can tell! He designed the one-of-a-kind houses that go along the Chicago River, the River Cottages. Their base, the three first floors, are conventional rectangular prisms, but the upper floors consist in a triangular prism with the hypotenuse facing the river. The slant roofs also present equilateral triangles forming a metal and glass alternating mosaic. Last but not least, take a look at the porthole style circular windows along the roof. Amazing!

Yes, we know, this one is not EXACTLY a triangular prism. Nevertheless, Lake Point Tower hides a triangular core that holds all of the vertical weight of the building as well as its three arms which form an asymmetrical Y-shaped floor plan. Those three arms are 120° apart and strategically curved so that the residents can’t peek inside their neighbour’s condo! From a farther point of view, you are looking at a beautiful concave based solid of revolution that seems to imitate the waves of Lake Michigan.

Other shapes…

The Chicago Mercantile Exchange Center is another impressive building. Its twin towers are separated enough to let the powerful breeze of the Windy City pass between them. We can’t forget its octagonal icon which represent the interior open outcry trading floor of the same shape.

The slope of this building is…

The Crain Communication Building’s unusual inclination allows to show the roof’s characteristic shape. That would explain its nickname, the Diamond Building. In fact, if you look close enough, you’ll see that the roof is not exactly in the shape of a diamond, but that the latter is separated in two almost identical triangles. Would you be able to calculate its slope?

Who said we needed right angles?

Mies Van Der Rohe, a well-known architect, has himself contributed to the reconstruction of the city of Chicago with his “skin and bones”, minimalistic style. He is mostly famous for his impressive structures of steel and plate glass, such as the Kluczynski Federal Building.

However, not everyone was thrilled with his style. One of his protégé rebelled against the “less is more” way of doing things, and created a more than original residential building without right angles! We instigated, and we still found some of them… can you?

Let’s do a little addition now, shall we?

It seems that buildings communicate in Chicago! We already introduced you to the Kluczynski Federal Building, well, right next to it are two tower that couldn’t be more at its opposite. Showing a cylindrical shape, they were designed to look like corn cobs! We can see the parking spaces in the lower part, and apartments with half-circle balconies constitute the upper part.

What’s our point? Well, we are glad that you ask! To an addition, one or the most simple algorithms! See for yourself… What do we get if we add the two building together?

We get the Aqua, the tallest building in the world with a woman as the lead architect, Jeanne Gang. The distinctive feature of this skyscraper stands in its irregularly shaped concrete floor slabs of almost 12 feet of width, which lend the facade an undulating quality inspired by the Great Lakes.

What about you? Have you ever observed buildings that demonstrate the use of mathematics in such a spectacular manner?