**ERIC Number:**ED214788

**Record Type:**Non-Journal

**Publication Date:**1979

**Pages:**84

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

UMAP Modules-Units 240-242, 251.

Horelick, Brindell; Koont, Sinan

Three of the modules deal with applications of calculus to other mathematics. These are: 240-Pi is Irrational; 241-The Wallis Approximation of Pi; and 242-Buffon's Needle Experiment. The first of these units focuses on a proof of the irrational nature of pi, and provides exercises and answers. The second module of this group reviews the history of attempts to calculate pi, and leads to a discussion of sequences in the Wallis formula, as originally discovered by the English mathematician John Wallis in about 1650. The third unit covers a "fun and games" method of approximating pi using needle tosses. The module gives a brief review of aspects of probability prior to discussing details of the experiment. A fourth unit in this document set focuses on applications of calculus to physiology and psychology: 251-A Strange Result in Visual Perception. The module describes an experiment on the process by which the eye sees bright light, and reviews the physiological background of eyes. A model is shown to predict seemingly paradoxical results. Exercises are presented at the conclusion to encourage further thought. Answers to these problems are included. (MP)

Descriptors: Calculus, College Mathematics, Higher Education, Instructional Materials, Learning Modules, Mathematical Applications, Mathematical Enrichment, Mathematical Models, Physiology, Probability, Problem Solving, Proof (Mathematics), Psychology, Supplementary Reading Materials, Visual Perception

**Publication Type:**Guides - Classroom - Learner

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**National Science Foundation, Washington, DC.

**Authoring Institution:**Education Development Center, Inc., Newton, MA.