Dear Math Circler,
There is one week left to register! Click the registration button below to sign up.
The Bard Math Circle is hosting the Purple Comet! math contest on Sunday, April 7th, 2019, from 1-3pm in the Reem-Kayden Center for Science and Computation on the Bard College Campus. Middle school students in teams of up to six students are welcome to compete. Also, parents and teachers will have the opportunity to join our non-competitive team.
The contest is 60 minutes long, with 20 questions at various levels of difficulty, all accessible to a middle school audience. After the competition we will all celebrate our collaborative mathematical achievements with pizza. Sign-up is absolutely free, click the 'Register' button below to be taken to a registration form.
We hope to see you next week!
A Perplexing Practice Problem from the Past
The diagram below shows a large square with each of its sides divided into four equal segments. The shaded square whose sides are diagonals drawn to these division points has area 13. Find the area of the large square.
(src: Purple Comet 2018)
Solution for the Perplexing Practice Problem from the Past:
The entire shape is made up of the following types of shapes: 5 squares, 4 large triangles that are half the area of the squares, and 4 small triangles that are half the area of the large triangles (or 1/4 of the area of the squares!). Since the area of each square is 13, the total area of the large square must be (5 x 13) + (4 x 0.5 x 13) + (4 x 0.25 x 13) = 65 + 26 + 13 = 104.