21. Esamskriti- Zero, PI, Geometry, Astronomy Essays on Indian culture,its history and its future.An analysis of Indianphilosophy,religion,vedanta,foreign affairs,the Kashmir problem,IndiaPakistan war http://esamskriti.com/html/new_inside.asp?cat_name=qanda&sid=175&count1=3&cid=10

22. Esamskriti- Introduction Chapters, Introduction, Origins, beliefs glory, Literature First University,Zero, pi, geometry, Astronomy, Surgery Contributions, Universal nature, http://esamskriti.com/html/new_inside.asp?cat_name=qanda&cid=1077&sid=175

23. Areas, Volumes, Surface Areas textellipse = pi r1 r2. texttriangle = (1/2) bh textsphere = (4/3) pir^{3}. textellipsoid = (4/3) pi r1 r2 r3 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

24. Circles Circumference of Circle = pi x diameter = 2 pi x radius where pi = pi = 3.141592 Area of Circle area = pi r2. Length of a Circular Arc (with central 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 = (

25. Surface Area Formulas Free math lessons and math homework help from basic math to algebra, geometryand beyond. Surface Area of a Cylinder = 2 pi r 2 + 2 pi rh http://www.math.com/tables/geometry/surfareas.htm

Home Teacher Parents Glossary ... Email this page to a friend Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search Surface Area Formulas Math Geometry pi Surface Area Formulas In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. Cube Rectangular Prism Prism Sphere ... Units Note: "ab" means "a" multiplied by "b". "a " means "a squared", which is the same as "a" times "a". Be careful!! Units count. Use the same units for all measurements. Examples Surface Area of a Cube = 6 a (a is the length of the side of each edge of the cube) In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared. Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac (a, b, and c are the lengths of the 3 sides)

26. Math Forum - Ask Dr. Math Archives: Middle School Pi Approximating pi using geometry 08/12/1998 I need to know a simple method tofind the approximate value of pi using elementary geometry. http://mathforum.org/library/drmath/sets/mid_pi.html

Ask Dr. Math Middle School Archive Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ TOPICS This page: pi Search Dr. Math See also the Dr. Math FAQ Pi = 3.14159... Internet Library pi T2T FAQ pi day MIDDLE SCHOOL About Math Algebra equations factoring expressions ... Word Problems Browse Middle School Pi Stars indicate particularly interesting answers or good places to begin browsing. Accuracy in Measurement Since pi is irrational, either the circumference or the diameter of a circle must be irrational. How is that possible? Calculating Pi - Brent-Salamin Algorithm Can you show me a simple method to calculate pi accurately to an arbitrary number of digits? Facts about Pi What are some interesting facts about pi? Finding Pi: Buffon's Needle Method I was hoping to find a surprising way of finding pi using a needle and parallel lines... Formula for Pi I would like to know the formula for Pi that was used to calculate out to the bazillionth digit for the memory contests. Pi and the Area of Circles If pi truly goes on and on forever without repeating, is it impossible to find the exact area of a circle?

27. Molecular Geometry - Wikipedia, The Free Encyclopedia Molecular geometry is determined by the type of bonds between the atoms that make the sigma bond; the pi bond. An understanding of these bonds is in the http://en.wikipedia.org/wiki/Molecular_geometry

Molecular geometry From Wikipedia, the free encyclopedia. Geometry of the water molecule Molecules have fixed equilibrium geometries — bond lengths and angles — that are dictated by the laws of quantum mechanics . The chemical formula and the structure of a molecule are the two most important factors that determine its properties, particularly its reactivity . Structure also plays an important role in determining polarity phase of matter color magnetism , and taste , among several other properties. Contents Bonding Isomers See also External links ... edit Bonding Molecules, by definition, are most often held together with covalent bonds involving single, double, and/or triple bonds, where a "bond" is a shared pair of electrons (the other method of bonding between atoms is called ionic bonding and involves a positive cation and a negative anion Molecular geometries can be specified in terms of bond lengths bonds angles and torsional angles . The bond length is defined to be the average distance between the centers of two atoms bonded together in any given molecule. A bond angle is the angle formed by three atoms bonded together. For four atoms bonded together in a straight chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms. Molecular geometry is determined by the type of bonds between the atoms that make up the molecule. Before atoms interact to form a

28. Math: Geometry: Pi Day | EThemes | EMINTS Learn the constant number pi = 3.14. Find out why it is celebrated on March 14thevery year. Discover why this number is considered to be a mysterious and http://www.emints.org/ethemes/resources/S00001525.shtml

About eMINTS Communities Equipment eThemes ... eThemes Math: Geometry: Pi Day Contact eThemes@emints.org if you have questions or comments about this resource. Printer-friendly version Please preview all links before sharing in class with students. Title: Math: Geometry: Pi Day Description: Learn the constant number Pi = 3.14. Find out why it is celebrated on March 14th every year. Discover why this number is considered to be a mysterious and fascinates some mathematicians. Learn how to calculate the number and use it for solving problems and equations. Includes animations, word problems, lesson plans, crafts, trivia, and quizzes. Grade Level: Resource Links: Oh, It's Pi Day! Find out how the Pi Day is celebrate by one middle school. Explore links on the page to view a list of activities and photographs. Click on the "Pi Trivia" link to test how much you know about pi. BrainPOP: Pi View this animated movie about the pi number in the Math section of the site to learn what pi represents, its history, and how to find this constant. Take a quiz after watching the movie and click on the "Bob, The Ex-Lab Rat" icon for a fun experiment. NOTE: The web site is available by subscription only. Pi Day This page has a number of activities for middle and high school students to celebrate the Pi Day.

29. Conjectures In Geometry: Circumference And "Pi" 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 http://www.geom.uiuc.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.

30. A Slice Of Pi Home Page This project studies how pi has been computed throughout history, includingcurrent connections between pi and geometry. A firsttime viewer should start http://www.geom.uiuc.edu/~huberty/math5337/groupe/welcome.html

A Slice of Pi This project studies how has been computed throughout history, including current connections between and geometry. A first-time viewer should start with the Historical Overview , which ties the project together as a timeline about . This Home Page gives a table of contents of all of the materials created in this project. Please note that the insctructions for using many of the Geometer's Sketchpad materials are given in the Web pages, not the sketches. Historical Overview of Pi Definition of Pi [Geometer's Sketchpad Sketch] Hippias' Quadratrix ... Return to the Math 5337 Home Page AUTHORS' E-MAIL AUTHORS' HOME PAGES http://www.geom.umn.edu/~huberty/math5337/groupe/ Created: March 1996 Last Modified: July 6, 1997

31. Space Figures And Basic Solids The surface area S of the sphere is given by the formula S = 4 × pi ×r2. Using an estimate of 3.14 for pi, the surface area would be 4 × 3.14 × 42 = 4 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.

32. Area And Perimeter The area of a circle is pi × r2 or pi × r × r, where r is the length of its Using an approximation of 3.14159 for pi, and the fact that the area of a 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

33. EGYPTIAN GEOMETRY - Mathematicians Of The African Diaspora geometry of ancient egypt. Until recently, Archimedes of Syracuse (250 BC)was generally consider the first person to calculate pi to some accuracy; http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egypt_geometry.html

EGYPTIAN GEOMETRY DETERMINING THE VALUE OF THE PYTHAGOREAN THEOREM Sacred Geometry? THIS PAGE IS UNDER CONSTRUCTION Unfortunately, a great many school children are misslead into believing as 3+1/8 using the observation below that the area of a circle of radius is "close to" the area of a square 8 units on a side. Until recently, Archimedes of Syracuse (250 BC) was generally consider the first person to calculate pi to some accuracy; however, as we shall see below the Egyptians already knew Archimedes (250B.C.) value of = 256/81 = 3 + 1/9 + 1/27 + 1/81, (the suggestion that the egyptians used = 3.1415 for <3+1/7 while in China in the fifth century, Tsu Chung-Chih calculate pi correctly to seven digits. Today, we "only" know to 50 billion decimal places Note 1 khet is 100 cubits, and 1 meter is about 2 cubits. A setat is a measurement of area equal to what we would call a square khet. An alternate conjecture exhibiting the value of is that the egyptians easily observed that the area of a square 8 units on a side can be reformed to nearly yield a circle of diameter 9. Rhind papyrus Problem 50 . A circular field has diameter 9 khet. What is its area. The written solution says, subtract 1/9 of of the diameter which leaves 8 khet. The area is 8 multiplied by 8, or 64 setat. Now it would seem something is missing unless we make use of modern data: The area of a circle of diameter

34. Geometry- Area Of A Circle pi. Every student will be introduced to this mysterious creature. That is it!!!Try geometry for more interesting concepts. Previous Articles http://math.about.com/library/weekly/aa111002a.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Homework Help ... Help w(' ');zau(256,140,140,'el','http://z.about.com/0/ip/417/C.htm','');w(xb+xb+' ');zau(256,140,140,'von','http://z.about.com/0/ip/496/7.htm','');w(xb+xb); FREE Newsletter Sign Up Now for the Mathematics newsletter! See Online Courses Search Mathematics PiR - It is Greek to me. A Different approach to the 'Area of Circle'. Math Tutorials Conic Sections Circles Circle Calculator (Area/Diameter) P i. Every student will be introduced to this mysterious creature. Everyone of them has been told that it represents the ratio of the circumference of a circle to the diameter. With that in mind, please understand that the area of a circle is equal to p r . Simple concept! Let's practice using this formula with the following worksheet, and by the way if it makes no sense, then memorize the formula and the fact that you feel 'dumb' is hidden from all. The ratio Pi ( p ) can be demonstrated and with some ingenuity the concept can become concrete using props and hands on . Using Pi

35. Thirteen Ed Online - Understanding Pi pi, Basic geometry, Irrational and Rational Numbers, Ratios Students will be ableto Measure the circumference of an object to the nearest sixteenth of an 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.

36. Is Pi Constant In Relativity? pi is a mathematical constant usually defined as the ratio of the circumferenceof a circle to its diameter in Euclidean geometry. http://math.ucr.edu/home/baez/physics/Relativity/GR/pi.html

[Physics FAQ] Original by Philip Gibbs 1997. Is pi constant in relativity? Yes. Pi is a mathematical constant usually defined as the ratio of the circumference of a circle to its diameter in Euclidean geometry. It can also be defined in other ways; for example, it can be defined using an infinite series: pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - . . . In general relativity, space and spacetime are non-Euclidean geometries. The ratio of the circumference to diameter of a circle in non-Euclidean geometry can be more or less than pi . For the types of non-Euclidean geometry used in physics the ratio is very nearly pi over small distances so we do not notice the difference in ordinary measurements. This does not mean that pi changes because our definition of pi specified Euclidean geometry, not physical geometry. No new theory or experiment in physics can change the value of mathematically defined constants.

37. Pi tall thin rectangles In Calculus, we may estimate pi by estimating the area ofa semicircle Jim s method Here is my own sleazy method for estimating pi. http://www.jimloy.com/geometry/pi.htm

Return to my Mathematics pages Go to my home page Pi , then click here for the alternative (Pi) page Definition of pi: What is pi (the symbol is the small Greek letter )? It is equal to C/d, or C/2r, where C is the circumference of any circle, and d is its diameter, and r is its radius. Euclid proved that this ratio (C/d) is always the same, no matter the size of the circle. What he did was inscribe similar regular polygons in any two circles. Then, he increased the number of sides of the inscribed regular polygons. He reasoned that as the number of sides increased, the perimeter of the inscribed polygon gets closer and closer to the circumference of the circle. He also showed that the perimeters of the similar polygons were proportional to the radii of the circles in which they were inscribed. And so, C is proportional to r, in other words C/r is a constant. By convention, pi=C/2r . And we can use that as our definition of pi. Definition of pi: pi=C/2r Since we know pi to many decimal places, the following version of the same equation becomes fairly useful: Circumference formula: C=2(pi)r Value of pi: Pi is about: Area of a circle: At the top of this article, I said that Euclid proved that C/2r is a constant. C/2r eventually became known as pi, and is our definition of pi. We need to figure out the area of a circle.

38. Geometric Shapes And Figures geometry is the mathematical study of shapes, figures, and positions in space . ratio between a circle s diameter and its circumference now known as pi. http://42explore.com/geomet.htm

var PUpage="76001074"; var PUprop="geocities"; var thGetOv="http://themis.geocities.yahoo.com/themis/h.php"; var thCanURL="http://us.geocities.com/kingfamilyaz/GeoShapesFigures.htm"; var thSpaceId="76001074"; var thIP="69.35.54.218"; var thTs="1100289832"; var thCs="a6afc8eb6430e10a90fa83a1d5920492"; The Topic: Geometric Shapes and Figures Easier - Circles, triangles, and squares are shapes. Geometry is the mathematical study of shapes, figures, and positions in space. It is useful in many careers such as architecture and carpentry. Harder - Geometry is the study of measurement and comparison of lines, angles, points, planes, and surfaces and of plane figures and solids composed of combinations of these. A shape is the outer form of an object or figure such as a circle, triangle, square, rectangle, parallelogram, trapezoid, rhombus, octagon, pentagon, and hexagon. There are equilateral, isosceles, and right triangles. A solid is a three-dimensional figure such as a cube, cylinder, cone, prism, or pyramid. Other solid shapes include the tetrahedron, octahedron, and dodescadhedron. Positions in space are things like points, lines, and angles. Formulas can be used to figure out the dimensions of shapes and figures. Instruments such as rulers, triangles, compasses, and protractors are used in geometry. Today, many people also use graphing calculators and computers in geometry.

39. Pi http//www.teachnet.com/lesson/math/geometry/circlesingeo.html Grade schoolgeometry doesn t have to get into a detailed lesson on pi to communicate http://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.

40. The Golden Geometry Of Solids Or Phi In 3 Dimensions Having looked at the flat geometry (two dimensional) of the number Phi, The angles in the rhombs in the Penrose tiling are 2/5 pi and 3/5 pi (72° and 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

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