I've always been a big fan of architecture, and while there are many types of architecture I enjoy, I have always been fascinated by twisted buildings. My trip to Saudi Arabia was planned at the last minute, and so I went in with almost no idea of what to expect. I was then pleasantly surprised when we came across the Al Majdoul Tower in Riyadh.

I think one of the reasons I've always loved twisted buildings is that their shapes are so unusual compared to what we normally see. In a high school geometry class you might see spheres, pyramids, cones, and rectangular prisms, all of which have simple formulas to calculate volume. But despite the complexity of these twisted buildings, calculating their volumes is actually relatively simple!

In Calculus II we learn that the volume of a shape can be calculated by integrating the cross-sectional area. But in this case, each cross-section is a square. So the cross-sectional area is constant. Therefore, we just need to multiply this cross-sectional area by the height of the tower to calculate its volume. In fact, this is the case for any twisted building with identical cross sections!

Another interesting calculation we can do is figure out the angle that each floor has twisted from the floor below it. To do this, we simply take the total rotation and divide by the number of floors! It's not complicated, but it's neat to compare how twisted different buildings actually are!