 The Shoelace Problem  Ivars Peterson (MathTrek)
How should shoes be laced? This seemingly simple question, rooted in everyday life, can provoke passionate argument  and evoke a mathematical response. There are at least three common ways to lace shoes, as illustrated: American (or standard) zigzag,
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 Shoe Size vs. Height  Statistical Analysis and Linear Regression with FATHOM  Jay Yohe; Susquehanna Township High School, Harrisburg, PA
A lesson plan in which students analyze onevariable distributions (histograms and box plots), determine measures of center (mean, median) and spread (standard deviation, range), analyze scatter plots, form lines of best fit, and explore least squares
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 A Short Course in Trigonometry  David Joyce; Dept. of Mathematics & Computer Science, Clark University
An introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations. Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and slope, the trigonometry of right
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 Shortest Enclosures on Surface of Cube (Math Chat)  Frank Morgan, MAA Online
The circle provides the leastperimeter way to enclose given area in the plane. What is the leastperimeter way to enclose given area in the surface of the unit cube? Answer: Al Zimmerman correctly finds that the best way to enclose small area is not
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 Should Nader Voters Flip a Coin? (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: Suppose that in a certain U.S. state 12 million potential voters favor Bush, 10 million favor Gore, and 5 million favor Nader with Gore as second choice. The Nader supporters want to be sure than Gore wins, but they would like
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 ShowTheMath.org  Alan Degener
Enter an algebra equation and then solve it, step by step  manually: use the pulldown menu to describe steps as combining like terms, distributing, expanding, factoring, adding to both sides, subtracting from both sides, dividing both sides, multiplying
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 Siemens STEM Academy  Siemens Foundation
The Siemens STEM Academy provides professional development to educators as they cultivate junior scientists who will pursue careers in science, technology, engineering, or mathematics (STEM). Opportunities include an annual STEM Institute; interactive
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 Siemens Westinghouse Competition  The Siemens Foundation
The Siemens Westinghouse Competition in Math, Science & Technology fosters individual growth for high school students seeking to challenge themselves through science research. Through this competition, students have an opportunity to achieve national
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 Sierpinski Shapes  Rick and Donna Joi
An interactive Java applet that allows you to create hundreds of fractal shapes using a variation of the Sierpinski triangle algorithm. Includes a page that provides a nontechnical explanation (with pictures) of the fractal math.
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 Sierpinski Tetrahedron: A Metal Sculpture  Stan Goldade
Pictures and background information on the sculpture, with some Sierpinski facts.
Breckenridge Senior High School students welded 4,096 equilateral metal triangles together to form 1,024 tetrahedra to form a stage5 Sierpinski Tetrahedron. It is located
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 The Sierpinski Triangle  Robert L. Devaney; Dept. of Mathematics, Boston University
Section from the paper "Chaos in the Classroom," describing the deterministic (rather than random) construction of the Sierpinski triangle.
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 Sieve of Eratosthenes  Interactive mathematics Miscellany and Puzzles, Alexander Bogomolny
Sieve of Eratosthenes with an interactive Java illustration. A slight
modification of the Eratosthenes' algorithm leads to a different sieve
that leaves out square numbers. The latter is also accompanied by a Java
illustration.
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 Sieve of Eratosthenes  Program in C
A class assignment for Mathematics 216: Introduction to Mathematical Computation (with C) at the Univ. of Utah. The new part of the C language learned was the array. Problems: Design a program to make a list of primes less than N = 100 using Eratosthenes'
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 Sifting through the Web's data jumble  Ivars Peterson; Science News Online
A combination of text and link analysis underlies a novel method based on analyses of the way Web pages are linked to one another for automatically generating lists of authoritative Web resources.
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 Sight Enhancement Systems
Manufacturers of large display scientific calculators with speech output, and of large display calculators that allow people with low vision to perform scientific, statistical and trigonometric calculations. Download brochures and manuals for the SciPlus
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 The Significance of the NCTM Standards to the Pathways (NCREL)  Cathy Cook; Pathways to School Improvement
Critical Issues in Mathematics. The Standards represent a major effort to develop mathematically literate citizens. They should be viewed as facilitators of reform, rather than as a set of directives. They are designed to help schools achieve national
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 Significant Digits  R. H. Logan, Instructor of Chemistry, El Centro College
An explanation of significant digits, with sections on: Measured Values; Computed Values; Rules for Determining the Number of Significant Digits In Numbers With Indicated Decimals; Significant Digits In Numbers Not Having an Indicated Decimal; Significant
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 Significant Figures and Rounding Rules  Christopher Mulliss
A site dedicated to the discussion of issues relating to the proper teaching of
significant figures and rounding rules in high school and college science courses. Includes a link to a detailed study "On the Standard Rounding Rule for Multiplication and
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 SI Guide  James R. Frysinger
SI (International System) measurements and quantities, with pages for: a basic starter set of units and prefixes; the unit compendium (a more complete list); the prefix compendium (a complete list); rules on usage (spelling, capitalization, spacing, plurals,
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 Silicon Champions of the Game  Ivars Peterson  Science News Online
Deep Blue's triumph over Gary Kasparov in May of 1997 marked the first match victory by a chessplaying computer over a reigning world champion. Some of the world's top computer programs are also playing backgammon, bridge, checkers, chess, Go, Othello,
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 The Silicon Mirror and Kaleidoscope  Elliot Leonard
The Silicon Mirror is an interactive tool for creating tessellations. It
operates on the same principles as a kaleidoscope. The Silicon Kaleidoscope is a screen saver that uses the Silicon Mirror to create kaleidoscopic images that flow in real time.
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 The Siluroid Curve  Dario de Judicibus
Formulas, graphs, compassandstraightedge constructions, derivatives, and more about this biquadratic, trilobate curve. Among the torpedo or fishshaped curve's curious properties: connecting its intersection with the generatrix or goniometric circle
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 SIMATH  Marc Conrad
A computer algebra system, especially for number theory. Try out the online version of the SIMATH calculator simcalc; a more detailed overview is available as a .dvi file or you can download the TeXSource of this file.
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 SimCalc Curriculum  James J. Kaput, Principal Investigator; Simulations for Calculus Learning
The SimCalc Project aims to democratize access to the Mathematics of Change for mainstream students. How the math of change can contextualize and organize many other important ideas already in the curriculum, moving to a strands structure that allows
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 SimCalc Library  James J. Kaput, Principal Investigator; Simulations for Calculus Learning
Papers and other writings on the SimCalc Project, which aims to democratize access to the Mathematics of Change for mainstream students: "Learning the Basics with Calculus"; "An introduction to the profound potential of connected algebra activities:issues
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 Simeon's World of Magic  Bob Fay
Interactive card tricks on the Web. Pick a card; whisper it out loud; Simeon will always remove it on the next page.
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 Similarity  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Scaling multiplies lengths by the same factor and produces a similar figure. It
preserves angles and
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 Similarity (SMILE)  Natalia Kee, Harlan Community Academy High School
A lesson designed to teach students to discover the factor of proportionality in similar polygons and relate this factor to the perimeters and areas of similar polygons. From the Geometry and Measurement section of a collection of almost 200 single concept
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 SIMMS IM LEVEL I  Research Project Help  T. DeBuff
High School freshmanlevel integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that will
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 Simple City  Richard Elwes
Website of the author of, among other books, Mathematics 1001, How to Build a Brain (Mathematics without the Boring Bits), and Chaotic Fishponds and Mirror Universes. Prior to lecturing at the University of Leeds, Elwes earned his PGCE (QTS) in secondary
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 Simple Minds, Smart Choices  Bruce Bower  Science News Online
The Center for Adaptive Behavior and Cognition at the Max Planck Institute for Human Development in Berlin has launched a project to explore the impact of bounded rationality on human judgment. The group focuses on what it calls "fast and frugal" formulas
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 Simplified Solutions for Math
Curricula (lesson plans, pratice work sheets and tests) for Algebra, CAHSEE, and General Math, aligned to the California Department of Education's Mathematics Framework for California Public Schools.
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 Simplifying Equations of the Form ax+b=cx+d (SMILE)  William F. Wagner, Hyde Park Career Academy
A lesson designed to teach students to solve equations of the form ax+b=cx+d; and to visualize the concept of "balancing" an equation. From the Algebra and Trigonometry section of a collection of almost 200 single concept lessons by the Science and Mathematics
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 Simply Statistics  Leek, Jeff; Peng, Roger; and Irizarry, Rafa
Biostatistics professors Leek, Peng, and Irizarry "are fired up about the new era where data are abundant and statisticians are scientists." Their blog, which dates back to September, 2011, has included posts such as "Precog and stats," "Kindle Fire
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 simpsonsmath.com  Sarah J. Greenwald and Andrew Nestler
The animated sitcom The Simpsons "contains over a hundred instances of mathematics, many designed to expose and poke fun at innumeracy," which make it "an ideal source of fun ways to introduce important concepts to students, and to reduce math anxiety
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 Simtel.Net  Digital River, Inc
A distribution network for shareware, freeware, and public domain software. Browse or search for programs running on the platforms of Windows 95/98, DOS, or Windows 3.x. Windows 95/98 mathrelated programs range from abacus instructional packages to an
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 Simulating Society  Ivars Peterson (MathTrek)
Computer simulation offers a powerful tool for studying human social behavior, contends Richard J. Gaylord of the University of Illinois at UrbanaChampaign. A theoretical physicist turned computational sociologist, Gaylord has developed models of social
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 Simulations Nab Proteinfolding Mistakes  Ivars Peterson  Science News Online
The human body manufactures thousands of different proteins, which act as enzymes, structural elements, or carriers. Each protein starts out as a long strand that must fold itself into the proper shape to perform its specific function. To gain insights
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 The Sine Function (SMILE)  Ronald G. Sienkiewicz, Prosser Vocational High School
A lesson designed to familiarize students with the concept of the sine function by defining, graphing, computer generating, using a "shop created" blackboard sine wave generator, and by presenting examples of natural phenomena which result in sine wave
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 Sine of the Times: Dividing the Universe by Zero  Colin Graham
A collection of thoughts on math by an "eternal student" with an "eclectic educational background." Posts, which date back to June, 2010, have included "Creative ways of integrating more water in the body," "My first online manipulative  virtual origami,"
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 Sines and Cosines, Part 1 (Periodic functions)  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related
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 Sines and Cosines, Part 2 (Trigonometry)  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. This program focuses on trigonometry, with special emphasis on the law of cosines and the law of sines,
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 Sines and Cosines, Part 3 (Addition formulas)  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy's
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 SingaporeMath.com Inc.
Formerly "Family Things," this family business located in Oregon, USA provides information, sample pages, and ordering information for the Singapore mathematics and science curricula, with sample placement tests for the New Elementary Math Series, sample
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 Singapore Math  Yan Kow Cheong
News and updates on Singapore Math from Cheong, a math coach, writer, editor, and life member of the Singapore Mathematical Society (SMS) and the Association of Mathematics Educators (AME) whose author credits include "Mathematical Quickies & Trickies."
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 singingbanana.com  James Grime
YouTube videos, "lazy microblog," and social networking hub of Enigma Project Officer James Grime, who "hopes to explain to kids and general audiences why he love his maths so much, to challenge some of the public's misconceptions, and to explain why
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 SINUS transfer  University of Bayreuth
Spurred by the outcome of the Trends in International Mathematics and Science Study (TIMSS), Germany launched a nationwide "model programme for increasing efficiency in mathematics and science education." Between 1998 and 2007, more than 1800 of the
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 Sir Roger Penrose  World of Escher
Recreational math is the passion of Sir Roger Penrose, who was recently knighted for his outstanding contributions to mathematics. Penrose is a professor of mathematics at the University of Oxford in England, where he pursues an active interest in recreational
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 Sir William Rowan Hamilton  D.R. Wilkins; School of Mathematics, Trinity College, Dublin
Material relating to Sir William Rowan Hamilton, including his letters and papers describing mathematical optics and conical refraction, dynamics, the theory of algebraic couples (complex numbers), the theory of equations, and quaternions; a memorial
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 SISA: Simple Interactive Statistical Analysis  Daan Uitenbroek
SISA is a collection of procedures for performing simple statistical calculations online, using HTML Forms. SISA's statistical tools include statistical procedures: (sequential probability, ratios, ttest, Fisher exact, two by two table, ordinal tests,
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