1. Creative Pi My Groups Language Help. Creative Pi. CreativePi@groups.msn.com pi geometry. pi geometry.bmp. pi geometry 2. pi geometry 2.bmp http://groups.msn.com/CreativePi/pirelatedpicturesplease.msnw

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2. Re:Sr-90 Source Activity/Geometry Sr90 only. Our crew is having a discussion about what the activity, in dpm, would be for 2 pi and 4 pi geometry. Also, if you are http://www.vanderbilt.edu/radsafe/9903/msg00750.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Re:Sr-90 Source Activity/Geometry To radsafe@romulus.ehs.uiuc.edu Subject : Re:Sr-90 Source Activity/Geometry From : "Rodney Bauman"< rodney_bauman@wssrap-host.wssrap.com Date : Wed, 24 Mar 1999 14:12:27 -0600 http://www.ehs.uiuc.edu/~rad/radsafe.html ************************************************************************ The RADSAFE Frequently Asked Questions list, archives and subscription information can be accessed at http://www.ehs.uiuc.edu/~rad/radsafe.html Prev by Date: RE: Three Mile Island Information Next by Date: Re: Guideline values for activity in Foodstuffs Prev by thread: RE: Sr-90 Source Activity/Geometry Next by thread: RE: Sr-90 Source Activity/Geometry -Reply Index(es): Date Thread

3. Discovering Pi TITLE Discovering pi AUTHOR Jack Eckley, Sunset Elem., Cody, WY GRADE LEVEL/SUBJECT 57, geometry OVERVIEW Many students tend to memorize, without understanding, formulas that we use in geometry http://www.col-ed.org/cur/math/math23.txt

TITLE: Discovering Pi AUTHOR: Jack Eckley, Sunset Elem., Cody, WY GRADE LEVEL/SUBJECT: 5-7, geometry OVERVIEW: Many students tend to memorize, without understanding, formulas that we use in geometry or other mathematic areas. This particular activity allows students to discover why pi works in solving problems dealing with finding circumference. OBJECTIVES: The students will: 1. Measure the circumference of an object to the nearest millimeter. 2. Measure the diameter of an object to the nearest millimeter. 3. Explain how the number 3.14 for pi was determined. 4. Demonstrate that by dividing the circumference of an object by its diameter you end up with pi. 5. Discover the formula for finding circumference using pi, and demonstrate it. RESOURCES/MATERIALS: round objects such as jars, lids, etc., measuring tapes, or string and rulers, paper, pencil, calculator ACTIVITIES AND PROCEDURES: 1. Divide class into groups of two. 2. Give materials to student teams. 3. Have student teams make a table or chart that shows name or number of object, circumference, diameter, and ?. 4. Have students measure and record each object's circumference and diameter, then divide the circumference by the diameter and record result in the ? column. 5. Have students find the average for the ? column and compare to other groups in the class to determine a pattern. Students can then find the average number for the class. 6. Explain to the students that they have just discovered pi, which is very important in finding the circumference of an object. (You may wish to give some historical information about pi at this time or have students research the information.) 7. Have students come up with a formula to find the circumference of an object knowing only the diameter of that object, and the number that represents pi. Students must prove their formula works by demonstration and measuring to check their results. TYING IT ALL TOGETHER: 1. Have students write their conclusions for the activities they have just done. Students may also share what they have learned with other members of the class. 2. Give students three problems listing only the diameter of each object and have them find the circumference. 3. Encourage students to share learned knowledge with parents.

4. ACTIVITIES INDEX geometry and Measurement Concepts( NCTM Content Standards and NCEE Standard M2) Students experiment with a simulation to get an approximation of pi. http://www.shodor.org/interactivate/activities

These activities listed below are designed for either group or individual exploration into concepts from middle school mathematics. The activities are Java applets and as such require a java-capable browser. The activities are arranged according to the NCTM Principles and Standards for School Mathematics and the NCEE Performance Standards for Middle School Number and Operation Concepts (NCTM Content Standard and NCEE Standard M1) Geometry and Measurement Concepts (NCTM Content Standards and NCEE Standard M2) Function and Algebra Concepts (NCTM Content Standard and NCEE Standard M3) Probability and Data Analysis Concepts (NCTM Content Standard and NCEE Standard M4) Each activity comes with supplementary What How , and Why pages. These pages are accessed from the activity page. Each will open in a new window, when its button is pressed. What: gives background on the activity; How: gives instructions for the activity; Why: gives curriculum context for the activity. See WHAT'S NEW in Interactivate! New Activities that are fully functional but do not yet have supporting materials developed.

5. History Of Mathematics - Table Of Contents Topics include background in Babylonian, Euclid, Al'Khwarizmi, pi, and trigonometry. Also has recreations and java chat. http://members.aol.com/bbyars1/contents.html

And Insights into the History of Mathematics Table of Contents Prologue The First Mathematicians The Most Famous Teacher Pi: It Will Blow Your Mind ... Comments and Notices

6. Areas, Volumes, Surface Areas textAreas, Volumes, Surface Areas. (pi = pi = 3.141592 ) textAreas. textcircle = pi r 2. textellipse = pi r 1 r 2. texttriangle = (1/2) bh. http://www.math2.org/math/geometry/areasvols.htm

[text:Areas, Volumes, Surface Areas pi = [pi] = 3.141592...) [text:Areas] [text:rectangle] = ab [text:parallelogram] = bh [text:trapezoid] = h/2 (b + b [text:circle] = pi r [text:ellipse] = pi r r [text:triangle] = (1/2) b h [text:equilateral triangle] = (1/4) [text:triangle given SAS] = (1/2) a b sin C [text:triangle given a,b,c] = [sqrt][s(s-a)(s-b)(s-c)] [text:when] s = (a+b+c)/2 ([text:Heron's formula]) [text:when n = # of sides and S = length from center to a corner] [text:Volumes] [text:rectangular prism] = a b c [text:irregular prism] = b h [text:cylinder] = b [text:pyramid] = (1/3) b h [text:cone] = (1/3) b [text:ellipsoid] = (4/3) pi r r r [text:Surface Areas] [text:prism]: ([text:lateral area]) = [text:perimeter]( b ) L ([text:total area]) = [text:perimeter]( b ) L + 2 b

7. Approximating Pi Using Geometry Approximating pi using geometry I need to know a simple method to find the approximate value of pi using elementary geometry. Ghosh http://rdre1.inktomi.com/click?u=http://mathforum.org/library/drmath/view/55034.

8. Circles origin the center of the circle pi ( ) A number, 3.141592 , equal to (the circumference) / (the diameter) of any circle. Area of Circle area = pi r 2. http://www.math2.org/math/geometry/circles.htm

Circles a circle Definition: A circle is the locus of all points equidistant from a central point. Definitions Related to Circles arc: a curved line that is part of the circumference of a circle chord: a line segment within a circle that touches 2 points on the circle. circumference: the distance around the circle. diameter: the longest distance from one end of a circle to the other. origin: the center of the circle pi ( A number, 3.141592..., equal to (the circumference) / (the diameter) of any circle. radius: distance from center of circle to any point on it. sector: is like a slice of pie (a circle wedge). tangent of circle: a line perpendicular to the radius that touches ONLY one point on the circle. diameter = 2 x radius of circle Circumference of Circle = PI x diameter = 2 PI x radius where PI Area of Circle: area = PI r Length of a Circular Arc: (with central angle if the angle is in degrees, then length = x (PI/180) x r if the angle is in radians, then length = r x Area of Circle Sector: (with central angle if the angle is in degrees, then area = (

9. Space Figures And Basic Solids If L is the length of a cylinder, and r is the radius of one of the bases of a cylinder, then the volume of the cylinder is L × pi × r 2 , and the surface http://www.mathleague.com/help/geometry/3space.htm

Space figures and basic solids Space figures Cross-section Volume Surface area ... Math Contests School League Competitions Contest Problem Books Challenging, fun math practice Educational Software Comprehensive Learning Tools Visit the Math League Space Figure A space figure or three-dimensional figure is a figure that has depth in addition to width and height. Everyday objects such as a tennis ball, a box, a bicycle, and a redwood tree are all examples of space figures. Some common simple space figures include cubes, spheres, cylinders, prisms, cones, and pyramids. A space figure having all flat faces is called a polyhedron. A cube and a pyramid are both polyhedrons; a sphere, cylinder, and cone are not. Cross-Section A cross-section of a space figure is the shape of a particular two-dimensional "slice" of a space figure. Example: The circle on the right is a cross-section of the cylinder on the left. The triangle on the right is a cross-section of the cube on the left. Volume Volume is a measure of how much space a space figure takes up. Volume is used to measure a space figure just as area is used to measure a plane figure. The volume of a cube is the cube of the length of one of its sides. The volume of a box is the product of its length, width, and height.

10. Area And Perimeter Area of a Circle. The area of a circle is pi × r 2 or pi × r × r, where r is the length of its radius. pi is a number that is approximately 3.14159. Example http://www.mathleague.com/help/geometry/area.htm

Area and perimeter Area Area of a square Area of a rectangle Area of a parallelogram ... Math Contests School League Competitions Contest Problem Books Challenging, fun math practice Educational Software Comprehensive Learning Tools Visit the Math League Area The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers. Area of a Square If l is the side-length of a square, the area of the square is l or l l Example: What is the area of a square having side-length 3.4? Area of a Rectangle The area of a rectangle is the product of its width and length. Example: What is the area of a rectangle having a length of 6 and a width of 2.2? Area of a Parallelogram The area of a parallelogram is b h , where b is the length of the base of the parallelogram, and h is the corresponding height. To picture this, consider the parallelogram below: We can picture "cutting off" a triangle from one side and "pasting" it onto the other side to form a rectangle with side-lengths

11. DOE Document - A 4$pi$ GEOMETRY DEVICE FOR STUDYING TIME CORRELATION A 4$pi$ geometry DEVICE FOR STUDYING TIME CORRELATION OF PHOTONS EMITTED BY VARIOUS GAS ATOMS. $$ http://rdre1.inktomi.com/click?u=http://www.osti.gov/energycitations/product.bib

12. The Topic Pi decimal. pie chart. double helix. pi cartoon. fractal. circle. pi video. circumference. pie. geometry. tessellation. pi Day . 159 pm March 14. pi. http://www.42explore.com/pi.htm

The Topic: Pi Easier - Pi sounds like pie and is equal to about 3.1416. In math, this is the ratio of the circumference of a circle to its diameter. In other words, pi is a number that equals the quotient of the circumference of a circle divided by its diameter. Many people celebrate pi by holding a Pi Day on March 14th or 3/14. Harder - The Greek letter pi represents the number by which the diameter of a circle must be multiplied to obtain the circumference. Pi is an irrational number. That is, it cannot be written as a simple fraction or as an exact decimal with a finite number of decimal places. However, you can increase the number of digits until you reach a number as near to pi as needed. Mathematicians with computers have calculated pi to millions of decimal places. Pi is used in several mathematical calculations. The circumference of a circle can be found by multiplying the diameter by pi (c = pi X d). The area of a circle is yielded by multiplying pi by the radius squared (A = pi X r-squared). Pi is also used to calculate the area of a circle, and the volume of sphere or a cone.

13. Conjectures In Geometry: Circumference And "Pi" Circumference and pi Conjecture. Explanation The circumference of a circle is the length around the edge of the circle. The diameter is a chord that passes through the center of the circle. Back Conjectures in geometry Conjecture List or to the Introduction http://www.geom.umn.edu/~dwiggins/conj49.html

Circumference and Pi Conjecture Explanation: The circumference of a circle is the length around the edge of the circle. The diameter is a chord that passes through the center of the circle. The radius is a segment from the center to any point on the circle. You are able to find the circumference once you have the measure of the diameter or the radius. We see that to find the circumference of a circle we need to use the number "pi". One exploratory way to find pi would be to measure the circumference of circles and divide by their diameters, respectively. You will find that pi is approximately equal to 3.14, or 22/7. Click here to further explore pi. The precise statement of the conjecture is: Conjecture ( Circumference If C is the circumference and D is the diameter of a circle, then there is a number p such that C=pD. Since D=2r, where r is the radius, the C=2pr. Interactive Sketch Pad Demonstration: Key Curriculum Press can provide demo versions of Geometer's Sketch Pad Sketchpad for Mac, Version 3.00 Sketchpad 3.04 for Windows More Sketch Pad download information Linked Sketch Pad demonstration of the Circumference Conjecture Linked Activity: Please feel free to try the activity sheet associated with this conjecture.

14. The Golden Geometry Of Solids Or Phi In 3 Dimensions The online book is worth browsing through as it has lots more interesting geometry about space The angles in the rhombs in the Penrose tiling are 2/5 pi and 3 http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi3DGeom.html

Some Solid (Three-dimensional) Geometrical Facts about the Golden Section Having looked at the flat geometry (two dimensional) of the number Phi, we now find it in the most symmetrical of the three-dimensional solids - the Platonic Solids. Contents of this Page The icon means there is a Things to do investigation at the end of the section. Phi and 3-dimensional geometry From 2-dimensional (flat) shapes, we turn to 3-dimensional ones (solids). Dice Shapes We need symmetry in dice if they are to be fair, but is the cube the only possible shape? No, there are 5 and only 5 fair dice shapes: Coordinates and other statistics of the 5 Platonic Solids The Tetrahedron The Cube or Hexahedron The Octahedron ... The Icosahedron Some other relationships between these shapes... The Dual of a Solid Golden sections in the Dodecahedron, Icosahedron and Octahedron A Cube in a Dodecahedron An Icosahedron in an Octahedron ... More Phi and 3-dimensional geometry The five regular solids (where "regular" means all sides are equal and all angles are the same and all the faces are identical) are called the five Platonic solids after the Greek philosopher and mathematician, Plato. Euclid also wrote about them. For more information on these two famous Greeks, see the

15. Two-dimensional Geometry And The Golden Section r = Phi 2 theta / pi. or r = M theta where M = Phi 2/pi. Such spirals, where The above is adapted from HSM Coxeter s book Introduction to geometry, 1961, page 165 http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi2DGeomTrig.html

Fascinating Flat Facts about Phi On this page we meet some of the marvellous flat (that is, two dimensional) geometry facts related to the golden section number Phi. A following page turns our attention to the solid world of 3 dimensions. Contents of this Page The icon means there is a Things to do investigation at the end of the section. Phi and 2-Dimensional geometry Constructing the golden section: phi Given any line AB, find a point G phi of the way along it. Constructing the golden section: Phi Given any line AB, make a new line AG which is Phi times as long. Phi and the Equilateral Triangle Use a hexagon in a circle to make an equilateral triangle and then you've already got a golden section point on a line! Phi and the Root-5 Rectangle A rectangle which is sqrt(5) wide and 1 unit high contains two golden rectangles. Pentagons and Pentagrams There are two kinds of triangles in pentagons and pentagrams, both have sides of length Phi and 1. Making a Paper Knot to show the Golden Section in Pentagons Flags of the World and pentagram stars The shape of a piece of paper "A" series Paper ... Phi and the Pentagon Triangles The two triangles of the pentagon and pentagram have some more interesting interactions involving Phi. Phi and another Isosceles triangle Decagons Penrose tilings Until recently, it was thought that there were no flat tilings that had five-fold symmetry, until Penrose discovered two tiles that do! These tilings involve the two pentagon/pentagram triangles and apply the relationships we found in the previous section.

16. Our Geometry/Pi Page HOUSE OF pie pi!!! Welcome one and all to our GeeI'm-A-Tree (geometry) and Trigonometry page. This is where you can get a list of Gee-I'm-A-Tree and Trigonometry postulates, theorems, laws, etc. Oh http://www.geocities.com/houseman_christina

HOUSE OF Pie Pi!!! Welcome one and all to our Gee-I'm-A-Tree (geometry) and Trigonometry page. This is where you can get a list of Gee-I'm-A-Tree and Trigonometry postulates, theorems, laws, etc. Oh, and of course, plenty of Pi... enjoy! Here are the links to the rest of our pages: GEOMETRY *Definitions of Geometry Terms* *Postulates* *Theorems* *Pi* ... *Examples of How To Do Geometry Problems* TRIGONOMETRY *Definitions of Trigonometry Terms* *Examples of How To Do Trigonometry Problems* Other Helpful Websites: *Introduction to Geometry* *Geometry Formulas and Facts* *Euclidian Axioms and Theorems* *Trigonometry and Astronomy* Need some help with your homework? Click here to send us your math question and/or suggestions! click on the arrow to go to the next page

17. Geometry Classes geometry Classes. Working in groups, students were asked to find solutions to the problems presented at seven stations. Back to the pi Day Page. http://www.nvnet.org/nvhs/dept/math/pi/geometry.html

Geometry Classes Working in groups, students were asked to find solutions to the problems presented at seven stations. They spent approximately ten minutes at each station over a period of two days. The stations were positioned in the classroom so that students could move from station to station in a clockwise fashion. Station 1 - Pool Problem Students are given the area of a circular pool and a distance from the edge where a circular fence will be constructed. They are to find the amount of fencing needed. Station 2 - National Park Problem Students are given sufficient information to find the circumference of a tree. They are to find the diameter of that tree. Station 3 - Shaded Region Problem Students are given three sketches involving the same square with a different number of circles within the square. They must determine which sketch has more shaded area. Station 4 - Windshield Wiper Problem Students are given the length of a windshield wiper, the length of a rubber wiping blade and the central angle of the sector. They must determine how much area is covered by the blade. Station 5 - Pizza Problem Students are given the diameter and the calories, per square unit, of a pizza. They must determine the measure of the central angle of a slice, given a restriction of number of calories per slice.

18. Pi Mu Epsilon pi Mu Epsilon. Purpose of the Organization of Interactive OnLine geometry. Computational geometry Resources. geometry Center. geometry Forum. geometry in Action http://www.tamiu.edu/student/pimuep

P i M u E psilon Purpose of the Organization Listing of Officers Adriana Chavarria, President Sonia Rodulfo, Vice-President Irma A. Ramirez, Secretary Deborah Cuellar, Treasurer Irma I. Ramirez, Public Relations Miguel San Miguel, Reporter Follow these links for math related resources on the WWW: Mathematics Organizations American Mathematical Society European Mathematical Society (EMS) Oxford University Invariant Society History of Mathematics History of Mathematics MacTutor History of Mathematics - A colection of over 550 biographies of mathematicians, 200 of which are quite detailed. Also a series of documents on the development of various branches of mathematics. Mathematics: Geometry A Gallery of Interactive On-Line Geometry Computational Geometry Resources Geometry Center Geometry Forum ... Geometry in Action - various areas in which ideas from discrete and computational geometry meet some real world applications. Geometry Literature Database Room 8 Geometry Book Wallpaper Groups Mathematics Numbers: 1,000,000 Digitsof e

19. Pi Day In geometry classes, students spent the two days working on investigations at seven stations . What better way to share the values of pi! http://www.nvnet.org/nvhs/dept/math/pi.html

Pi Day While the middle of March is most renown as the ides of March, for the Mathematics Department of Northern Valley Regional High School March 14 (3.14) is "Pi Day". Since pi to four decimal places is 3.1415, March 15 is "Little Pi Day". To celebrate these days, mathematics teachers organized some unconventional activities revolving around the importance of pi. In Geometry classes, students spent the two days working on investigations at seven "stations". Twice during the course of the day, three teachers mixed their classes so that groups working at the "stations" comprised students from different ability groups. What better way to share the "values" of pi! Pizza "pis" were seen in several teachers' classes, as well as "pi" snacks (sugar free, of course). Pi Day is the invention of Demarest mathematics teacher Pat Karpinski, and each year it is becoming a bigger and bigger event. This year, mathematics teachers Debra Baker, Danielle DeFuria, Jim Hall, Mike McElduff, Ray Siegrist, and April Vella participated in the Pi Day activities, as could be evidenced their Pi Day T-Shirts. (Sorry, these are collectors' items and cannot be purchased.) Anyone interested in receiving worksheets, etc. should contact

20. Math Forum: Basden: The Derivation Of Pi Math Forum Ask Dr. MathI need to know a simple method to find the approximate value of pi using elementary geometry. Approximating pi using geometry. Date http://mathforum.org/te/exchange/hosted/basden/pi_3_14159265358.html

A Math Forum Web Unit Jon Basden The Derivation of (Pi) May I Have A Large Container of Coffee Jon Basden's Lessons Teacher Exchange TE: Grades 6-8 Grade Level 7th Grade Illinois Learning Standards 6.B.3a Solve practical computational problems involving whole numbers... 6.B.3c Identify and apply properties of real numbers, including pi... 7.B.3 Select and apply instruments including rulers... and units of measure to the degree of accuracy required. 7.C.3b Use concrete and graphic models and appropriate formulas to find perimeters... of two-dimensional... figures. Approximate Time Two forty minute class periods Materials Required six or so circular objects of various sizes string meter sticks paper pencils student worksheets overhead transparency of student worksheet computer with spreadsheet program Optional Materials Pre-made spreadsheet in Microsoft Excel 97 Math Madness cassette tape the Pi Song (Can order from Bob Garvey for $8.50 at bgarvey@aol.com First 1001 digits of Pi on overhead transparency Sources Modifications of: "Discovering Pi" lesson from Math in the Middle Handbook, Prentice Hall, 1993

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