Math Project Recommendations

Date: 07/16/97 at 08:13:36
From: Sagar Sen
Subject: Math Project

Dr. Math:

I have a project to be made this year. I'm in grade 11. Please suggest 
some interesting projects for me.

Thanks.

Date: 07/16/97 at 13:55:54
From: Doctor Dan
Subject: Re: Math Project

Sagar, 

I am glad that you are interested in a mathematics project.  You did 
not mention what area of mathematics you were working in or any 
personal interests you might have. You might consider whether you can 
take an area you already have an interest in (soccer for example) and 
build a mathematics project around it (for example you might look at 
the growth of interest in soccer over the past twenty years as 
measured by participation in public recreation leagues and/or shoe 
sales). 

I have reproduced below a list of possible mathmatics projects which I 
have used with my own students. Most of these topics are geometrical 
in nature but if you check the references you will find a world of 
additional possibilities and ideas.

I hope that I have been of some help as you think about what you'd 
like to do.

MATH PROJECT SELECTION LIST
      
 1. Investigate the five "perfect" (or Platonic) solids and explain 
why there are only five. References: "The Mathematics Teacher", April 
'77, p. 335.

 2. Research an invention based on unusual geometric properties or  
configurations (e.g. Rolamite Bearing, Wankel Engine, Holograms, 
etc.). References: "Popular Science", Feb. '76, p. 106;  "Popular 
Science", Aug. '76, p. 84; "Scientific American", Aug. '72, p. 15;  
Edmund Scientific Catalog; Student Math Notes, March 1989, Consortium 
Fall 1995(#55).

 3. Learn about the Escher variety of periodic drawings and learn how 
to analyze an Escher drawing to find the unit cell, etc. References: 
"The Mathematics Teacher", April '74,; "The Mathematics Teacher", Dec. 
'76, p. 647.                     

 4. Investigate tiling the plane with similar figures (tessellation). 
References: "Scientific American", July '75, p. 112; "Scientific 
American", Aug. '75, p. 112; Sachs, ed. Student Merit Awards, pp. 
108ff.  

 5. Analyze and describe the construction of an accurate sundial 
(gnomon). Reference: "The Mathematics Teacher",  May '75, p. 438; 
Waugh, Sundials, Their Theory and Construction, '73, New York, Dover. 

 6. Make and use a clinometer (sextant) to indirectly measure five 
lengths. Do this project only after having studied similar triangles.  
Reference: "The Mathematics Teacher", Feb. '76, p. 135.

 7. Investigate the field of topology. References: Life Science 
Library, Mathematics, pp. 176-191; Sharp, A New Mathematics Reader 
(JML), Chapter 11;  "The Mathematics Teacher", Mar. '76, p. 215;  "The 
Mathematics Teacher", Dec. '75, p. 647; Sachs, ed. Student Merit 
Awards, p. 34 ff; NCTM, Enrichment Mathematics for High School; 
Francis, The Mathematician's Coloring Book, COMAP; Student Math Notes, 
Nov. 1990

 8. Research the application of mathematical principles in the world 
of art with a written description of those principles and their 
application. References: "The Mathematics Teacher", April '77, p. 298; 
also February '91, p 133; The Life Science Library, Mathematics, pp. 
84-10, Consortium #46.

 9. Make a display and write a report on ancient number systems. 
References: "The Mathematics Teacher", May '75, p. 393; Life Science 
Library, Mathematics, Chapter 1; "The Mathematics Teacher", April '76, 
p. 296; Sachs, ed. Student Merit Awards, p. 130. Chance, Rhind 
Mathematical Papyrus. 

10. Investigate the connection between economics and math. References:  
"The Mathematics Teacher", Mar. '75, p. 189; "The Mathematics 
Teacher", Sept. '79, p. 450; "The Mathematics Teacher", Feb. '79, 
p. 134; Kastner, Applications of Secondary School Mathematics, pp. 
49ff.  

11. Investigate and report on financial institutions and simulate 
investing in the stock market.  References: "The Mathematics Teacher", 
Sept. '77, p. 493; HiMAP module in Consortium Fall '95.

12. Investigate and report on the careers of architect, civil 
engineer, and  land surveyor. Reference: "The Mathematics Teacher", 
Sept. '77,  p. 495.

13. Research the role of geometric shapes and properties in 
architecture and  construction. Reference: A fine example of this kind 
of display can be found in the Life Science Library, Mathematics, 
pp. 94 ff. 

14. Calculate the average distance to a McDonald's. Consortium #34 
(Summer, 1990); Student Math Notes, March 1988.

15. Archimedes. Reference: Sachs, ed. Student Merit Awards.

16. Pythagoras and His Theorem, Reference: Sachs, ed. Student Merit 
Awards. 

17. Music and Mathematics. Reference: Kastner, Applications of 
Secondary School Mathematics. Maor, "What is there so Mathematical 
about Music?" from "The Mathematics Teacher"  Sept '79, pp 414-422; 
O'Shea, "Geometric Transformations and Musical Composition." from "The 
Mathematics Teacher" '72, PP 523-528,  Garland and Kahn, Math and 
Music,  (510 GAR)

18. Minimal surface experiments with soap bubbles.

19. Ciphers, Codes and the way they are broken Reference: The 
Mathematical Tourist, "An Application of Number Theory to Cryptology", 
"The Mathematics Teacher", Jan '89, p.18. "The Mathematics Teacher" 
Jan 91, "The Mathematics Teacher" Dec '96 p 743, also Oct 1984; 
Consortium Winter 1991; Malkevitch, Loads of Codes, COMAP; Consortium 
#37 p 3.

20. Investigate the Golden Proportion and the Golden Rectangle in art 
and nature. Reference: "The Mathematics Teacher" Nov. '96 p. 680.

21. How Eratosthenes Measured the circumference of the earth.

22. The theory of perspective in drawing: Consortium # 46.

23. Measurement of the distance from the earth to the moon by simple 
geometry.  Reference: Project STAR, Where We Are in Space and Time, 
Unit II, Activity 7.

24. Statistics. Reference: Sachs, ed. Student Merit Awards.

25. Non-Euclidean Geometry. Many attempts have been made to prove 
Euclid's fifth postulate, all unsuccessful.  A system of geometry that 
is  constructed without the use of the Parallel Postulate is known as 
a non-Euclidean geometry.  What is absolute geometry? hyperbolic 
geometry? elliptical geometry?  Reference: Courant, What is 
Mathematics? New York: Oxford University Press, 1978; Insights into 
Modern Mathematics. Twenty-third Yearbook of the National Council of 
Teachers of Mathematics. Washington, D.C.: The Council, 1957; 
Consortium #53. "The  Mathematics Teacher" Sept 1980, April 1977, Sept 
1985, Oct 1977.

26. Fibonacci Numbers. In 1202 the mathematician Fibonacci wrote about 
a problem concerning the breeding of rabbits. The pattern of 
population growth under the given constraints formed a sequence now 
known as a Fibonacci Sequence, famous for its applications in many 
fields of mathematics and nature. The Phyllotactic ratio .Reference: 
Brown, "From the Golden Rectangle and Fibonacci to Pedagogy and 
Problem Posing." "The Mathematics Teacher" 69: 180-188; Dalton, Topics 
for Mathematics Clubs. 2nd ed. Reston, VA: National Council of 
Teachers of Mathematics, 1983; Gardner. "The Multiple Fascinations of 
the Fibonacci Sequence." Scientific American, Vol. 220  No. 3, pp 116-
120; March, 1969

27. Investigation Beyond the Third Dimension. We perceive our world as 
one of three dimensions. Mathematicians of vision, however, have 
ventured beyond these limits, conceptualizing "spaces" of four and 
even more dimensions. How can we use algebra and geometry to extend 
our knowledge of the first three dimensions? Can you build a model of 
a tesseract, the fourth-dimensional equivalent of a cube? Reference: 
Abbot. Flatland. Many editions; Burger. Sphereland. (trans. by 
Rheinboldt) Scranton, PA: Apollo Editions (distributed by Harper and 
Row Publishers, Inc. NY); Henry. "The Fourth Dimension and Beyond... 
with a Surprise Ending!" "The Mathematics Teacher" 67:274-279; Hess. 
Four-Dimensional Geometry Reston, VA: National Council of Teachers of 
Mathematics, 1977; Manning. The Fourth Dimension Simply Explained. New 
York: Dover Publications, 1960; Marr. 4-Dimensional Geometry, Boston: 
Houghton Mifflin Company, 1970;  Sommerville. An Introduction to 
Geometry of N Dimensions, New York: Dover Publications,1958; 
http://www.students.uiuc.edu/~ferrar/java/hypercuber/HyperCuber.html   .

28. Some Special Numbers. The constants 0, 1, i, and e  have many  
important and unique properties. What are these numbers?  How are they  
related to each other?  How did they develop in the history of  
mathematics? References: Bell. Men of Mathematics. New York: Simon and 
Shuster, 1937; Gardner. "Mathematical Games." Scientific American, 
Vol. 241, No 2, pp. 18-24; June, 1976; Historical Topics for the 
Mathematics Classroom. Thirty-first Yearbook of the National Council 
of Teachers of Mathematics, Washington, D.C.: The Council, 1969; 
Kasner. Mathematics and the Imagination. New York: Simon and 
Shuster,1940; Mathematics in the Modern World: Readings from 
"Scientific American." San Francisco: W.H.  Freeman and Co., 1968; 

29. Use a spreadsheet program on the computer to investigate 
mathematical formulas. Reference: "The Mathematics Teacher" 85, 
May 1992, pp 346-347.
               
30. Investigate the use of check digits and error detecting codes in 
use today. UPC bar coding, Social Security numbers, etc. References: 
"Consortium"  Spring, 1987; "Consortium" Summer 1987;  Mlkevitch. 
Codes Galore, COMAP

31. Investigate the curvature of surfaces. References: "The 
Mathematics Teacher", February '94.

32. Explore Fractals and objects having non-integral dimensions. 
References: Student Math Notes, Nov 1991; Consortium #41 and 45; "The 
Mathematics Teacher" Jan '97 p. 35.

33. Game Theory. Investigate the application of mathematics to game 
strategies.  Zero-sum games, etc.  References:  Student Math Notes: 
May 1987. Consortium #52.

34. Investigate the technique of linear programming. "Consortium"  
Winter 1991 and Summer 1992.

-Doctor Dan,  The Math Forum
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