This site provides a nice description of how pi is calculated via the use of the arctangent function and leads to a connection with the Fibonacci numbers. It includes material on various well-known approximations for pi based on infinite series interspersed with Things to Do sections that invite the reader to explore the material in more depth. Some research problems are presented at the end of the expository material along with links to related sites and a list of references. This site is a subpage of Fibonacci Numbers and the Golden Section that is reviewed separately in MERLOT.
Type of Material:
Lecture/presentation plus hands-on calculations.
Recommended Uses:
Student exploration or enrichment.
Technical Requirements:
Standard Web browser.
Identify Major Learning Goals:
To develop student understanding of the arctangent function and its relationship to the value of pi; to lead students to investigate and explore numerical patterns and to develop proofs.
Target Student Population:
High school and college math students.
Prerequisite Knowledge or Skills:
General knowledge of trig functions and sequences/series is helpful.
Content Quality
Rating:
Strengths:
The content is accurate and of interest to the general math student. The page uses a considerable amount of trigonometry, and several computations involving arctangent formulas before reaching the connection with the infinitely many formulas using Fibonacci Numbers. There is also a link to a page with over two hundred general formulas that involve Fibonacci numbers. Many exercises for calculator or computer are included and will encourage interactive use of the page. The reference section includes both paper and electronic entries.
Concerns:
None
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The materials are well-written and accessible to all high school and college math students. Everyday examples are used effectively, such as discussion of the steepness of a road and how it might be calculated in two different ways. The Research Problems would possibly interest math majors; the History of Computing Pi site listed as a related Web site provides excellent background info on pi. The Things to Do sections provide excellent directions to students who are interested in pursuing investigations.
Concerns:
None
Ease of Use for Both Students and Faculty
Rating:
Strengths:
No technical difficulties were encountered in the use of this site. The site is visually attractive with good use of color, icons and graphics.
Concerns:
One Two of the external links in More Links and References was were inactive, viz., Solidz website and University of Exeter. Typos in Wetherfields Notation section: ahvenoticed and mathematicains. Some of the references to historical mathematicians are linked to the St. Andrews biography site (eg: Gregory) but many others are not (eg: Pythagoras, Machin, Euler).
Creative Commons:
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