Download the two winning essays to learn about using indivisibles to find the area under a cycloid arch in the 17th century and about the Radon transform and its use in x-ray tomography in the 20th century.
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?