41. Geometry 101 Example #5 Inspection of the geometry indicates a solution between pi/4 and pi/3 where theupper bound is determined from the equation x=acos(a/2r) when a = r. The http://pw1.netcom.com/~essoft/geometry.html

Geometry 101 Previous Example Next Example This academic exercise is a static problem which goes something like this: A friendly neighbor gave Johnny permission to tie his goat on the perimeter of his circular pasture provided that no more than half of the pasture is grazed. How long should that rope be? pi*a^2*(x/pi) + [pi*r^2*(y/pi) - a*r*sin(x)] = pi*r^2/2 (a/r)^2*x + (pi - 2x) - (a/r)sin(x) = pi/2 2xcos(x)^2 - sin(x)cos(x) - x = -pi/4 The first equation defines the desired surface area of the overlapping circles contoured by the radius r and chord a respectively. A bit of algebra and the angular identity y = pi - 2x produces the second equation. The final equation follows a substitution for the ratio a/r = 2cos(x) which calculates the rope length once the angle x is known. Solving the nonlinear equation for x with, say, Newton-Raphson method, is a quick option for a programmable calculator or a canned PC math package. Here however, we highlight the simple mechanism with which the "solver" interacts with the system to be solved. call nlsq (isol

42. Expressions - Geometry Math.asin(number), 1 to 1, -pi/2 to pi/2, -90° to 90°. Math.acos(number), -1 to1, 0 to pi, 0° to 180°. Math.atan(number), -inf to inf, -pi/2 to pi/2, -90° to90°. http://www.jjgifford.com/expressions/geometry/inverse_functions.html

Vector Addition Distances and Lengths Trigonometry Graphs: sine, cosine and tangent ... Inverse Functions OTHER MATERIAL Introduction to Expressions Tables Project Index Home Inverse Funtions: Arcsine, Arccosine and Arctangent The inverse functions tell you which angle would produce the value you've specified with the corresponding trigonometric function. For instance, arcsine(n) gives you the angle whose sine equals n. Like the other trigonometric functions, the inverse functions belong to the Math object. The table below shows how each of these functions is written, the range of values it accepts, and the range of values it can produce, given in both radians and degrees: Inverse Function Input Range Results, in radians in Degrees Math.asin(number) -1 to 1 -Pi/2 to Pi/2 Math.acos(number) -1 to 1 to Pi Math.atan(number) -inf to inf -Pi/2 to Pi/2 Math.atan2(y, x) -inf to inf, 2D -Pi to Pi Remember that tangent = opposite / adjacent. So if you were to use the number form of arctan, you'd write something like: temp=opposite/adjacent;

43. D&M Pyramid - Geometry The aforementioned ambiguity concerning e/pi vs. the square root of three dividedby two can be resolved with the geometry of a circumscribed tetrahedron. http://www.well.com/user/etorun/geometry.html

Evaluation The D&M Pyramid appears to be positioned with architectural alignment to other enigmatic objects nearby that have also been studied as possibly artificial. The main axis of the D&M as illustrated above points at the Face in Cydonia. Henceforth we will refer to this direction as the "front" of the pyramid. The front of the D&M Pyramid has three edges, spaced 60 degrees apart. As noted above, the center axis points to the Face. The edge on the left of this axis points toward the center of a feature that has been nicknamed the "City" by the Cydonia investigators. The edge on the right of the center axis points toward the apex of a dome-like structure known as the "Tholus". The five-sidedness, bilateral symmetry, and primary alignments were first observed by Richard Hoagland after studying quality digital enlargements prepared in 1984 by SRI International from negatives of images processed by DiPietro and Molenaar. These events are documented in detail by Hoagland and Pozos Turning back to the reconstructed geometry, we will now consider the internal symmetries of this object.

44. Is Pi Constant In Relativity? measurements. This does not mean that pi changes because our definitionof pi specified Euclidean geometry, not physical 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.

45. Computational Geometry Tutorial Computational geometry Tutorial. To view the applet, click here. If yourconnection is slow, download can take a while (say few minutes). http://www.imc.pi.cnr.it/~javacg/

Computational Geometry Tutorial To view the applet, click here . If your connection is slow, download can take a while (say few minutes). To grant the applet privileges to open/save files, you must perform the following steps: create a CGTutorial folder in your home directory; set an appropriate .java.policy file, again in your home; restart the applet. Alternatively, you can download the tutorial and run it as a standalone application ( java -jar CGTutorial.jar bartolet@di.unipi.it CGTutorial comes with ABSOLUTELY NO WARRANTY; This is free software, and you are welcome to redistribute it under certain conditions; see the GNU General Public License for details.

46. Solution For /geometry/hole.in.sphere Solution to the /geometry/hole.in.sphere problem. The It is pi * (D/2)^2.The same area as a circle with that diameter. Proof big http://rec-puzzles.org/sol.pl/geometry/hole.in.sphere

Solution to the /geometry/hole.in.sphere problem The volume of the leftover material is equal to the volume of a 6" sphere. First, lets look at the 2 dimensional equivalent of this problem. Two concentric circles where the chord of the outer circle that is tangent to the inner circle has length D. What is the annular area between the circles? It is pi * (D/2)^2. The same area as a circle with that diameter. Proof: big circle radius is R little circle radius is r 2 2 area of donut = pi * R - pi * r 2 2 = pi * (R - r ) Draw a right triangle and apply the Pythagorean Theorem to see that 2 2 2 R - r = (D/2) so the area is 2 = pi * (D/2) Take a general plane at height h above (or below) the center of the solids. The radius of the circle of intersection on the sphere is radius = srqt(3^2 - h^2) so the area is pi * ( 3^2 - h^2 ) For the ring, once again we are looking at the area between two concentric circles. The outer circle has radius sqrt(R^2 - h^2), The area of the outer circle is therefore pi (R^2 - h^2) The inner circle has radius sqrt(R^2 - 3^2). So the area of the inner circle is

47. Solution For /geometry/cover.earth Solution to the /geometry/cover.earth problem. We know that V = (4/3)*pi*r^3 andA = 4*pi*r^2. We need to find out how much V increases if A increases by 1 m^2 http://rec-puzzles.org/sol.pl/geometry/cover.earth

Solution to the /geometry/cover.earth problem We know that V = (4/3)*pi*r^3 and A = 4*pi*r^2. We need to find out how much V increases if A increases by 1 m^2. dV / dr = 4 * pi * r^2 dA / dr = 8 * pi * r dV / dA = (dV / dr) / (dA / dr) = (4 * pi * r^2) / (8 * pi * r) = r/2 = 3,250,000 m If the area of the cover is increased by 1 square meter, then the volume it contains is increased by about 3.25 million cubic meters. We seem to be getting a lot of mileage out of such a small square of cotton. However, the new cover would not be very high above the surface of the planet about 6 nanometers (calculate dr/dA). E-mail to the index to Arlet's home page Linux ... Apache ... ``follow me,'' the wise man said, but he walked behind...

48. Geometry Review geometry Review. We have used several simple facts here A triangleinscribed in a semicircle, as shown below, is a right triangle. http://personal.bgsu.edu/~carother/pi/geometry.html

Geometry Review We have used several simple facts here: A triangle inscribed in a semicircle, as shown below, is a right triangle. [Proof] [Return to Archimedes' method] Given triangle inscribed in semicircle , as shown below, the central angle is twice the angle [Proof] [Return to Archimedes' method] [Main Index] [Pi Index] ... Neal Carothers - carother@bgnet.bgsu.edu

49. Geometry Review geometry Review, Part I. A triangle inscribed in a semicircle is a right triangle.In the picture below we want to show that angle is a right angle. http://personal.bgsu.edu/~carother/pi/geometry-p1.html

Geometry Review, Part I A triangle inscribed in a semicircle is a right triangle. In the picture below we want to show that angle is a right angle. One way to see this is to take advantage of Cartesian coordinates: Here we've identified our semicircle with the top half of the graph of To check that is a right angle, we will show that the Pythagorean theorem is satisfied for this triangle (with the diameter of our circle as the hypoteneuse of the right triangle). In terms of our coordinates: [Return to geometry review] [Return to Archimedes's method] [Main Index] [Pi Index] ... Neal Carothers - carother@bgnet.bgsu.edu

50. Enumerative Real Algebraic Geometry: Bibliography P. PEDERSEN AND B. STURMFELS, Mixed monomial bases, in Algorithms in Algebraic Geometryand Applications pi, M. piERI, Sul problema degli spazi secanti, Rend. http://www.math.umass.edu/~sottile/pages/ERAG/bibliography.html

Up: Table of Contents Bibliography [Be] D. N. B ERNSTEIN The number of roots of a system of equations , Funct. Anal. Appl., 9 (1975), pp. 183-185. [BGG] I. N. B ERNSTEIN, I. M. G ELFAND, AND S. I. G ELFAND Schubert cells and cohomology of the spaces G P , Russian Mathematical Surveys, 28 (1973), pp. 1-26. [Ber] A. B ERTRAM Quantum Schubert calculus , Adv. Math., 128 (1997), pp. 289-305. [Br] R. B RICARD [BCS] P. B URGISSER, M. C LAUSEN, AND M. S HOKROLLAHI Algebraic Complexity Theory , Springer-Verlag, 1997. [COGP] P. C ANDELAS, X. C. DE LA O SSA, P. S. G REEN, AND L. P ARKES A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory , Nuclear Phys. B, 359 (1991), pp. 21-74. [Ca] G. C ASTELNUOVO Numero delle involuzioni razionali gaicenti sopra una curva di dato genere , Rendi. R. Accad. Lineci, 4 (1889), pp. 130-133. [CE-C] R. C HIAVACCI AND J. E SCAMILLA- C ASTILLO Schubert calculus and enumerative problems , Bollettino Un. Math. Ital., 7 (1988), pp. 119-126. [Cl] J. C

51. Geometry Connects Jean's Pi Return Column Navigator Jean's pi Sorry, this page requires a Javacompatibleweb browser. Investigating pi. Drag point A or B http://www.math.vt.edu/people/hagen/Registration/Spring2001java/Jeans_Pi.html

Investigations Return Column Navigator: Jean's Pi Sorry, this page requires a Java-compatible web browser. Investigating Pi Drag point A or B to change the size of the diameter. Notice that changing the size of the diameter (and therefore the circle), has no effect on their ratio. Do you recognize this number? Result..... Circumference divided by the Diameter will always result in pi. Return Last Updated: 05/29/2000 Email: Susan Hagen

52. Geometry & Measurement http//www.sisweb.cum/math/geometry/areavols.htm This website is a table of formulasfor area, surface area Websites about pi (contributed by Nicole Brockman). http://www4.ncsu.edu:8030/~hsdrier/ems480/spr2001/geommeasure.html

Teaching Middle and Secondary School Mathematics with Technology Annotated Website Resources compiled by Spring 2001 Class Members GEOMETRY AND MEASUREMENT Area, Surface Area, and Volume (contributed by Kristina Young) http://daniel.calpoly.edu/~dfrc/Robin/X-38/X38-index.html This website contains a lesson plan for 7 th and 8 th grade teachers that discusses how doubling the sides of a figure does not necessarily double the area and volume. It uses the X-38 and the X-33, which are two NASA vehicles, as the examples. This lesson may be used as an interdisciplinary lesson and the interesting NASA vehicles may be useful in motivating students’ participation. http://www.highland.madison.k12.il.us/jbasden/lessons/circle_area.html This website contains a lesson on area of a circle. This lesson uses the idea of cutting a circle into wedges and rearranging them to create a parallelogram. It also relates finding the area of a parallelogram to finding the area of a circle. http://www.thetech.org/people/teachers/resources/activities/inn/package.htm This website contains a 5 th through 8 th -grade lesson on surface area. Students are asked to design a box that a pair of one-size fits all gloves will fit in. The box must also be cost effective. This lesson gives students a real world example of how surface area is used.

53. Pi - Wikipedia The number pi (denoted with the lowercase Greek letter p) is a mathematical constant ratioof a circle's circumference to its diameter in Euclidean geometry. http://www.wikipedia.org/wiki/Pi

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Deutsch Esperanto Polski Pi From Wikipedia, the free encyclopedia. The number pi (denoted with the lower-case Greek letter ) is a mathematical constant which occurs in many areas of mathematics and physics . It is also known as Archimedes ' constant or Ludolph's number and is equal to the ratio of a circle 's circumference to its diameter in Euclidean geometry area of a circle of radius 1, or as the smallest positive number x for which sin x Properties irrational number : that is, it cannot written as the ratio of two integers . This was proved in by Johann Heinrich Lambert . In fact, the number is transcendental , as was proved by Ferdinand Lindemann in . This means that there is no polynomial with integer (or rational This result establishes the impossibility of squaring the circle : it is impossible to construct, using

54. EGYPTIAN GEOMETRY - Mathematicians Of The African Diaspora Sacred geometry? Until recently, Archimedes of Syracuse (250 BC) was generally considerthe first person to calculate pi to some accuracy; however, as we shall 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

55. REC Research PI Survey Answers REC Research pi Survey Answers. Award 0133619 Year 2002 Title CAREERReasoningin High School geometry Classrooms Understanding the Practical Logic http://www.ehr.nsf.gov/rec_survey_report/detail.asp?id=0133619

56. Geometry - Patterns - Themepark What did the little acorn say when he grew up? geometry . pi Day Page http//planetpi.8m.com/Start making plans now to celebrate your own pi Day http://www.uen.org/themepark/html/patterns/geometry.html

Tessellations General Math Fractions/Decimals Geometry ... Patterns Geometry Geometry is the branch of mathematics that involves studying the shape, size, and position of geometric figures. These figures include plane (flat) figures, such as circles, triangles, and rectangles, and solid (three-dimensional) figures, such as cubes, cones, and spheres. The name geometry comes from two Greek words meaning earth and to measure. The world is full of geometric shapes and patterns. Sample some of the following activities to learn more about geometry. Places To Go People To See Things To Do Teacher Resources ... Bibliography Places To Go The following are places to go (some real and some virtual) to find out about geometry. Geometry Center http://www.scienceu.com/geometry/ Visit the Geometry Center. It has interactive activities, geometry articles, and classroom help. A Look at 3D Geometry http://library.thinkquest.org/2842/3d_geometry/ Travel to the pyramids of Egypt (http://www.ancientegypt.co.uk/pyramids/index.html) and check out their angles. Then learn more about prisms and pyramids.

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

Home Teacher Parents Glossary ... Email this page to a friend Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search Circles Math Geometry a circle D efinition: 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 =

58. Surface Area Formulas Surface Area Formulas. (Math geometry Surface Area Formulas). (pi= = 3.141592 ). Surface Area Formulas In general, the surface 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)

59. Pi Mu Epsilon Action various areas in which ideas from discrete and computational geometry meetsome there are many interesting constants in mathematics other than pi and e http://www.as.ysu.edu/~math/pme/links.htm

Mathematics Organizations American Mathematical Society European Mathematical Society (EMS) 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. Peek: For Visualizing > 3-dimensional objects Wallpaper Groups Mathematics Numbers: Favorite Mathematical Constants - These essays aim to show that there are many interesting constants in mathematics other than pi and e. Googoolplex List of the Largest Known Primes - contains record primes of various primes as well as links to pages on primality proving... PI Pi [ucla.edu] - just in case all the other sites are down and you REALLY need to know pi. The first 500,000 digits of PI

60. 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;

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 3     41-60 of 188    Back | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | Next 20