**ERIC Number:**EJ819414

**Record Type:**Journal

**Publication Date:**2008

**Pages:**8

**Abstractor:**ERIC

**Reference Count:**5

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

Problem Solving in Calculus with Symbolic Geometry and CAS

Todd, Philip; Wiechmann, James

Australian Senior Mathematics Journal, v22 n2 p49-56 2008

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical expressions can be copied back and forth between a symbolic geometry system and a CAS thus making it an interesting new tool for exploring mathematics and solving problems. In this paper, the authors illustrate the use of a symbolic geometry system applied to two classic optimisation problems, both drawn from "100 Great Problems of Elementary Mathematics". The first problem, "Regiomontanus' Optimisation Problem", is suitable for students at the upper secondary level. The second, "Fagnano's Perimeter Minimisation Problem", does involve some partial derivatives, and so would be more suitable for students at tertiary level. Their symbolic geometry system is "Geometry Expressions" (Saltire Software, 2008). In order to illustrate the flexibility of the CAS interface, in the first problem the authors use "Mathematica" (Wolfram Research, 2008), and in the second problem, they use "Maple" (Maplesoft, 2008). (Contains 10 figures.)

Descriptors: Computer Software, Geometry, Calculus, Algebra, Problem Solving, Mathematics Instruction, Computer Uses in Education, Symbols (Mathematics), Geometric Concepts, Secondary School Mathematics, College Mathematics

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

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

**Education Level:**Higher Education; Secondary Education

**Audience:**Students; Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A