A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
After completing this assignment on Simon Stevin's treatment of decimal fractions in his 1585 De Thiende, the author's preservice mathematics teachers understood why our usual procedure for multiplying such fractions works.
Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.