**ERIC Number:**EJ775306

**Record Type:**Journal

**Publication Date:**2003-Sep

**Pages:**5

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5785

Just Four Points and "The Prepared Mind"

Sharp, John

Mathematics Teaching, n184 p8-12 Sep 2003

Solving problems often means trying out ideas one knows about which might lead down blind alleys. In this article, the author provides a solution to the following simple mathematical problem: Suppose you have four points which are on the four sides of a square, how do you construct the square? He says that the obvious place to tackle it is to use the property that the angle in a semi-circle is a right angle. However, one soon finds that this approach does not get the desired result. Solving a problem like this requires building up a bank of knowledge to call upon, hence "the prepared mind." Lessons to be learned from the experimentation required to solve this four points problem are discussed. (Contains 6 figures and 9 resources.)

Association of Teachers of Mathematics. Unit 7 Prime Industrial Park, Shaftesbury Street, Derby, DE23 8YB, UK. Tel: +44-1332-346599; e-mail: admin@atm.org.uk; Web site: http://www.atm.org.uk/mt/index.html

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A