A recent NY Times puzzle (http://wordplay.blogs.nytimes.com/2011/05/02/numberplay-sameweight/) has a problem asking if areas C and D have the same weight when balanced as in the following picture
A number of solutions have been submitted, but I decided to provide one.
See PlanetPTC for a full solution and downloadable Mathcad worksheet.
The idea is simple: use a double integral to compute both areas/weights:
and moments of segments C and D:
Solve for total moment to be 0
to find the balancing point:
Use the balancing point to verify that the weights are not the same:
About Bettina Giemsa
I graduated from Ruhr University in Bochum, Germany, with a Master of Arts in American Studies, Japanese, Economics * Started my career in Marketing on the agency side, spending almost 3 years in media planning * Ran Marketing at ITEDO Software GmbH, Germany from 2001-2006 where I first got in touch with the CAD business * Became part of the PTC Marketing organization when ITEDO was acquired by PTC in October 2006 * Last, but not least, I am the mother of a 4-year-old, and sometimes wonder which is harder to cope with: a little girl with a temper or a busy workday…
