81. ENC Online: ENC Features: Classroom Calendar: Pi Day (Grades 6-12) An applet for middle and high school geometry students that lets them investigate Archimedes computation of pi graphically and interactively. http://www.enc.org/features/calendar/unit/0,1819,34,00.shtm

Skip Navigation You Are Here ENC Home ENC Features Classroom Calendar Search the Site More Options Classroom Calendar By Category By Month ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Pi Day (Grades 6-12) March 14 Graphic: Brian Deep Because pi (the ratio of the circumference of a circle to its diameter) is an important concept in mathematics and science, March 143/14has been proclaimed as a special "pi day." Scientists have explored the concept of pi, an irrational number, beginning perhaps as far back as 4000 years ago and continuing right up to the present. Early evidence of the use of pi can be found in civilizations ranging from Ancient Babylon to Greece, Egypt, and China. In fact, some time between A.D. 430 and 501, a Chinese astronomer estimated pi to a value that was so accurate that it took a thousand years before its accuracy was matched in Europe. In 1596, a Dutch mathematician helped to expand the calculation of pi to 35 places by figuring out three more digits. It is said that he had those three digits, 388, inscribed on his tombstone. With the advent of the computer, pi has been calculated to over 51 billion decimal places! Connections Here are just a few suggestions for making the day special:

82. Geometry In The Natural World geometry IN. THE NATURAL WORLD. The Golden Mean, or Golden Ratio as it is known, is an irrational number just like other important numbers such as pi. http://www.infinitetechnologies.co.za/articles/geometry1.html

GEOMETRY IN THE NATURAL WORLD The Golden Mean: The Golden Mean, or Golden Ratio as it is known, is an irrational number just like other important numbers such as Pi. This means that it cannot be completely represented by our currently used number system, except as a formula ( Sqr (5)-1)/2. Just like Pi (approx. 3.1416) - Phi, or the Golden Ratio, has an endless number of digits after its decimal point and with no repetition of the digits sequences. Therefore, like other "Transcendental" numbers, its value can only be approximated (using our number system). What is the Golden Ratio, and why is it important? The Golden Ratio is approximately Besides for possessing some remarkable and unique characteristics, the Golden Mean is found in ALL living creatures on Earth. Along with the Fibonacci Sequence (which is a whole-number system approximating the Golden Ratio, discovered by Leonardo Pisano Fibonacci), this ratio is found in plants and animal life wherever one looks. For example, this ratio can be found in fingers one's hand, amongst many other places, and it is prevalent in the skeletal structure of all creatures. The Fibonacci Sequence is as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...

83. Sekeds From this it is clear that the measure of the hypotenuse was an aspect of Ancient Egyptian mathematics and geometry which had practical pi and the cubit. http://www.kch42.dial.pipex.com/sekes.htm

Sekeds and the Geometry of the Egyptian Pyramids A comparison between the angles generated by sekeds and the angles of gradient of the pyramids This article looks at the relationship of the seked to the design of the pyramids of Ancient Egypt with particular reference to the pyramids of the IIIrd to VIth dynasties. It argues that whilst the seked can be clearly perceived in some pyramids it would appear that in others a different, or modified, system was used to calculate their angles of slope. Sekeds Information on the use of the seked in the design of pyramids has been obtained from two mathematical papyri; the Rhind Mathematical papyrus in the British Museum and the Moscow Mathematical papyrus in the Museum of Fine Arts. The Rhind Mathematical Papyrus ( hereafter referred to as RMP ) was copied by the scribe Ahmose c.1650BC and is based on a document two hundred years earlier1. Problems 56 to 60 in the RMP deal specifically with calculating the seked of different pyramids, or the height of a pyramid when the seked is known. The seked is based on the Ancient Egyptian measures of the Royal Cubit, the palm or hand and the digit. The relationship of these measures is as follows:

84. ESCOT geometry, measurement, number operations. Components AgentSheets, logoscript, HTML viewer, text editor, swing slider, simple number table, number entry. pi http://www.escot.org/resources/standards/geometry.html

Algebra Geometry Measurement Geometry National Council of Teachers of Mathematics Standards 2000 URL: http://standards.nctm.org/document/chapter6/geom.htm For all grades, NCTM standards focus on students being able to: "analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; apply transformations and use symmetry to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems " understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;

85. Thirteen Ed Online - Understanding Pi Grade Level 79 Subject Matter Mathematics Curricular Uses pi, Basic geometry, Irrational and Rational Numbers, Ratios Students will be able to Measure the http://www.thirteen.org/edonline/lessons/pi/

Understanding Pi Students learn the mathematical value of pi through the process of measuring circumference. Students conduct hands-on calculations for cylindrical objects, demonstrate the properties of a circle, and discover for themselves how pi works. Grade Level: Subject Matter: Mathematics Curricular Uses: Pi, Basic Geometry, Irrational and Rational Numbers, Ratios Students will be able to: Measure the circumference of an object to the nearest sixteenth of an inch. Measure the diameter of an object to the nearest sixteenth of an inch. Explain why 3.14 is used as an approximation for pi. Demonstrate why one may compute pi by dividing the circumference of an object by its diameter. Discover and apply the formula for calculating the circumference of an object by using pi. Learn the definitions of rational and irrational numbers and see specific examples of each. Understand why pi is an irrational number. Use of Internet: The Internet is used as a research tool. It also helps students see and hear visual and musical representations of pi. This lesson was developed by Emily Crawford, Linda George, and Tracy Goodson-Espy.

86. Commencement Math pi, Students justify the procedures for basic geometric constructions. pi, Students apply axiomatic structure to algebra and geometry. http://www.nyiteez.org/MPNYA/mathcommence.htm

new york web alignment ~ mathematics marcopolo ny mathematics MST Standard Three: Mathematics Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry. Key Idea Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument. PI Students construct simple logical arguments. Lesson Four: Gallery Walk Generating and Analyzing Data PI Students follow and judge the validity of arguments.

87. Baseball . For Teachers . Baseball Geometry | PBS the formula for the surface area of a sphere is S = 4 * pi * r^2. Baseball geometry Bloom Quiz 1. How many footprint shaped pieces are stitched together to http://www.pbs.org/kenburns/baseball/teachers/lesson4.html

Introduction Shadow Ball Bases Divided Baseball Memories Baseball Geometry Download PDF Crossing the Line: Jackie Robinson The Best of the Best Stadium Consultants ... Related PBS Lessons BASEBALL GEOMETRY Grade: Subject: Mathematics Background: Over the many years that baseball has been played, the ball itself has undergone many changes. Materials used inside and out have been tested, alternately resulting in advantages to pitchers and to batters. This lesson will explore the specifications of the modern baseball. Objectives: Students will: be introduced to historical and modern materials and construction of baseballs apply various methods for finding volume and surface area of a sphere compare and contrast results among these methods Estimated Time: Two or more 50-minute periods (one for generating and collecting data for surface area and volume; one or more for each Extension activity). Materials Needed: Play-Doh wax paper baseballs overhead transparency with square centimeter grid. Baseball innings Shadow Ball, The National Pastime and The Capital of Baseball (recommended but not required) Resources listed below Procedure: 1) Give every student a baseball for the activity. (The local Little League coaches can help you out here by loaning the baseballs temporarily for the activity, suggesting a source for purchasing a class set at the best price.)

88. Ethnomathematics Digital Library (EDL) numerals, and Jaina mathematics. Other terms calculus, pi, geometry. (Includes 28 references). Subject Cultural Context Cultural http://www.ethnomath.org/search/browseResources.asp?type=subject&id=445

89. Institute For Mathematics And Its Applications (IMA)- Homepage Hua Lu University of Arizona, Introduction to Symplectic and Poisson geometry. 2002 IMA pi Summer Program for Graduate Students Scientific Computing University http://www.ima.umn.edu/PI/summergrad.html

Search Contact Information Program Registration Postdoc/Membership Application Program Feedback ... Join our Mailing Lists IMA Participating Institutions Graduate Student Summer Program The IMA pioneered the Graduate Student Summer Program in 1990 and manages it for the IMA Participating Institutions. Each year this program brings together a selected group of mathematics students from the IMA Participating Institutions at one of the PI campuses for intensive study in a particular area. During the program, which typically lasts two to four weeks, lecture series are given on several related topics by senior mathematicians. The students live together in a dormitory and participate in a social program as well. Funding for the lecturers and student living expenses, for up to two students from each Participating Institution, are assumed by the IMA. The goals of this program are: To expose graduate students to a selected set of exciting topics.

90. Geometry In Action Includes collections from various areas in which ideas from discrete and computational geometry meet real world applications. http://www.ics.uci.edu/~eppstein/geom.html

This page collects various areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications. It contains brief descriptions of those applications and the geometric questions arising from them, as well as pointers to web pages on the applications themselves and on their geometric connections. This is largely organized by application but some major general techniques are also listed as topics. Suggestions for other applications and pointers are welcome. Geometric references and techniques General geometric references Related applications pages Patents in geometric applications Constraint solving ... Delaunay triangulations , and medial axes Design and manufacturing Architecture Assembly planning Computer aided design Computer aided manufacturing ... VLSI design Graphics and visualization Computer graphics Graph drawing Virtual reality Video game programming Information systems Cartography and geographic information systems Data mining and multidimensional analysis Medicine and biology Biochemical modeling Biology Medical imaging Sequence alignment Physical sciences Astronomy Molecular modeling Scientific computation Robotics Computer vision Grasp planning Robot motion planning Other applications Character recognition Compiler design Control theory Signal processing ... UC Irvine Last update: 14 Jan 2001, 09:34:01 PST

91. Course Information Lecture notes by Alain Connes. http://www.math.ohio-state.edu/connes/Connes_course.html

Noncommutative Geometry, Trace Formulas and the Zeros of the Riemann Zeta Function Abstract In this course we first give a general introduction to noncommutative geometry. We then discuss a fundamental example of noncommutative space related to the Riemann zeta function. This gives a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while the noncritical zeros appear as resonances, and a geometric interpretation of the explicit formulas of number theory as a trace formula on a noncommutative space. This reduces the Riemann hypothesis to the validity of the trace formula, which remains unproved, and eliminates the parameter of our previous approach. Topics Introduction to noncommutative geometry Quantum chaos and the hypothetical Riemann flow. Algebraic geometry and global fields of nonzero characteristic. Spectral interpretation of critical zeros. The distribution trace formula for flows on manifolds. The action of K on K for a local field. The global case, and the formal trace computation. The trace formula and S -units.

92. E-zgeometry.com For high school teachers and students. Products include an interactive textbook, class video clips, projects, glossary, and resource links. http://www.e-zgeometry.com/

Geometry Projects, Geometry Links, Glencoe Geometry Textbook Notes, Geometry Glossary, High School Geometry Project Ideas, Interactive Geometry Experiences, Geometer's Sketchpad Applets, Geometry Video Footage and much more

93. Books By Jean-Pierre Demailly Book by JeanPierre Demailly in PostScript. http://www-fourier.ujf-grenoble.fr/~demailly/books.html

Books by Jean-Pierre Demailly (last update: November 10, 2000) Complex analytic and algebraic geometry I just got cancelled a stupid agreement I signed long ago with a publisher. This means that my book will soon be available as an "OpenContent Book", i.e. that you can get the source file for free and do whatever you like with it on the web (print it, spread it, modify it, etc...) except claiming that you are the author! At the moment, it is still not completely achieved and the TeX file is not polished enough. Instead, here is a (compressed) PostScript file of the current version: agbook.ps.gz

94. [physics/9709045] An Introduction To Noncommutative Geometry A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics. http://arxiv.org/abs/physics/9709045

Physics, abstract physics/9709045 From: "Joseph C. Varilly" [ view email ] Date: Tue, 30 Sep 1997 22:38:08 GMT (91kb) An Introduction to Noncommutative Geometry Authors: Joseph C. Varilly Comments: 85 pages, Plain TeX, lectures at EMS Summer School on NCG and Applications, Sept 1997 Report-no: UCR-FM-12-97 Subj-class: Mathematical Physics; Differential Geometry; Quantum Algebra These are lecture notes for a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997. 1. Commutative geometry from the noncommutative point of view. 2. Spectral triples on the Riemann sphere. 3. Real spectral triples, the axiomatic foundation. 4. Geometries on the noncommutative torus. 5. The noncommutative integral. 6. Quantization and the tangent groupoid. 7. Equivalence of geometries. 8. Action functionals. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

95. Sacred Geometry Home Page Sacred geometry is an ancient art and science which reveals the nature of our relationship to the cosmos. Its study unfolds the principle of oneness underlying all creation in its myriad expression, and leads us inevitably to the perspective of interconnectedness, inseparability and union. http://www.intent.com/sg/

Sacred Geometry Home Page by Bruce Rawles In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created. The Sphere (charcoal sketch of a sphere by Nancy Rawles) Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm. The Circle The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

96. The Geometry Junkyard Usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry. http://www.ics.uci.edu/~eppstein/junkyard/

These pages contain usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry. Some of it is quite serious, but I hope much of it is also entertaining. The main criteria for adding something here are that it be geometrical (obviously) and that it not fit into my other geometry page, Geometry in Action , which is more devoted to applications and less to pure math. I also have another page on non-geometrical recreational math Junk sorted into piles All the junk in one big pile New junk ... UC Irvine Semi-automatically filtered from a common source file. Last update: 07 Jun 2004, 16:14:25 PDT.

97. Geometric Formulae Review V sph = ( 4 / 3 )(pi)r 3. Some instructors like to give all needed geometric formulas, so your test will have a listing of anything you might need. http://www.purplemath.com/modules/geoform.htm

Purplemath — Your Algebra Resource Geometric Formulae Review Lessons Home There are many geometric formulas, relating height, width, length, or radius to perimeter, area, surface area, or volume. Some of the formulas are rather complicated, and you hardly ever see them, let alone use them. But there are some basic formulas that you really should have memorized, because it really is reasonable for your instructor to expect you to know them. For instance, it is very easy to find the area of a rectangle: the area is just the length l times the width w A rect lw If you look at a picture of a rectangle, and remember that "perimeter" means "length around the outside", you'll see that a rectangle's perimeter is the sum of the top and bottom lengths l and the left and right widths w P rect l w Squares are even simpler, because their lengths and widths are identical. The area and perimeter of a square with side-length s are given by: A sqr s P sqr s You really should know the formula for the area of a triangle; it's easy to memorize, and tends to pop up unexpectedly in the middle of word problems. Given the measurements for the base

98. EIMI: Arithmetic Geometry Conference Euler International Mathematical Institute, St Petersburg, Russia; 2026 June 2004. http://www.pdmi.ras.ru/EIMI/2004/AG/

International conference ARITHMETIC GEOMETRY June 20-26, 2004 St Petersburg, RUSSIA SCIENTIFIC COMMITEE Ch.Deninger (director of SFB, Muenster) I. Fesenko ( Nottingham ) A.Parshin ( Moscow ) S.Vostokov ( St. Petersburg ) ORGANIZING COMMITEE S.Vostokov ( St. Petersburg ) A.Parshin ( Moscow ) I.Panin ( St. Petersburg ) M.Bondarko ( St. Petersburg ) LIST OF SPEAKERS Amnon Besser Ben Gurion Yuri Bilu Bordeaux Michael Bondarko St. Petersburg Ted Chinburg Pennsylvania Joachim Cuntz Muenster Christopher Deninger Muenster Ivan Fesenko Nottingham Luc Illusie Paris-Sud Kazuya Kato Kyoto Toshiyuki Katsura Tokyo Nobushige Kurokawa Tokyo Falko Lorenz Muenster Loic Merel Paris Bernardus Moonen Amsterdam Tetsuo Nakamura Tohoku Alexei Parshin Moscow Vladimir Popov Moscow Christophe Soule Bures Sur Yv Martin Taylor Manchester Sergei Vostokov St. Petersburg Jean-Pierre Wintenberger Strasbourg Gisbert Wuestholz ETH Zurich Yuri Zarhin Penn State Further information First conference on arithmetic geometry Back to the EIMI home-page Back to the Petersburg Department of Steklov Institute of Mathematics

99. Buy Pi A Source Book By Lennart Berggren At Walmart.com pi A Source Book by Lennart Berggren in Hardcover. ISBN 0387989463. pi is one of the most interesting and wellknown numbers in all of mathematics. This new edition of a definitive http://rdre1.inktomi.com/click?u=http://na.link.decdna.net/n/3532/4200/www.walma

100. Area/Perimeter/Volume Word Problems Some problems are just straightforward applications of basic geometric formulae of each end is given by the area formula for a circle with radius r A = (pi)r 2 http://www.purplemath.com/modules/perimetr.htm

Purplemath — Your Algebra Resource Geometric Word Problems Lessons Home The trick to these problems is to note that, unless it's a simple application of basic geometric formulae, they will almost always give you two pieces of information, such as a statement about perimeter and then a question about area. Then you need to write the two equations related to these two pieces of information, solve one of the equations for one of the variables, and then plug this into the other equation. Here are some examples: Three times the width of a certain rectangle exceeds twice its length by three inches, and four times its length is twelve more than its perimeter. Find the dimensions of the rectangle. The first statement compares the length L and the width W . Start by doing things orderly, with clear and complete labelling: three times the width: W twice its length: L exceeds by three inches, meaning "is three inches greater than": equation: W L Now I have the second statement, which compares the length

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