**ERIC Number:**EJ1231087

**Record Type:**Journal

**Publication Date:**2018

**Pages:**7

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

**EISSN:**N/A

An Easier Derivation of the Curvature Formula from First Principles

Ferguson, Robert

Australian Senior Mathematics Journal, v32 n2 p16-22 2018

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier way to motivate and prove the radius of curvature formula without using formal calculus. An additional benefit is that the proof provides the coordinates of the centre of the corresponding circle of curvature. Understanding the proof requires only what advanced high school students already know: e.g., algebra, a little geometry about circles, and the intuition that both a circle and a curve have a slope and curvature. The proof is suitable for first-year university and advanced high school students.

Descriptors: Mathematics Education, Algebra, Geometry, Mathematical Logic, Mathematical Formulas, Problem Solving, Mathematics Instruction, Teaching Methods, 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:**Secondary Education; Higher Education; Postsecondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A