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Pi Geometry: more books (26)

Why is pi?: A short treatise on proportionate geometry by Thomas F Black, 1974
The Joy of Pi by David Blatner, 1997-12-01
The Wallis approximation of [pi]: Applications of calculus to other mathematics (UMAP modules in undergraduate mathematics and its applications) by Brindell Horelick, 1989
Pi: A Source Book
Bragg Curve Spectroscopy in a 4pi Geometry by D. A.; et al Cegra, 1990
Program guide and workbook to accompany the videotape on the story of PI by Tom M Apostol, 1989
The Wallis approximation of [pi] (UMAP module) by Brindell Horelick, 1979
The Number Pi by Pierre Eymard, Jean-Pierre Lafon, 2004-02-06
Pi - Unleashed by Jörg Arndt, Christoph Haenel, 2001-01-25
Sir Cumference And The Dragon Of Pi (Turtleback School & Library Binding Edition) by Cindy Neuschwander, 1999-04-01
Pi, the reciprocal of seven and trigono/metrix (Essays from Earth/matriX : science in ancient artwork) by Charles William Johnson, 1999
Pi: A Biography of the World's Most Mysterious Number by Alfred S. Posamentier, Ingmar Lehmann, 2004-08-31
The Foundations of Geometry and the Non-Euclidean Plane by G.E. Martin, 1982-03-22
Easy as Pi?: An Introduction to Higher Mathematics by Oleg A. Ivanov, 1998-12-04

lists with details

Human Form From Sacred Geometry
became very interested in the three dimensional representation of this geometry and I to find that by multiplying the inner sphere s diameters by pi gives the
http://saturn.vcu.edu/~chenry/

Extractions: Richmond, Virginia This site is best viewed on Microsoft Internet Explorer 4.0 or higher with screen set to 1024 X 768 pixels, 24 bit ...16 million colors. Set ... View/Text Size ... to Meduim Click on thumbnails to view larger images. For more than twenty years, I have been studying the image generating properties of reflective spheres stacked in 52 degree angle pyramids. The 52 (51.827) degree angle slope of the sides of The Great Pyramid in Cairo, Egypt embodies the Golden Mean which is the ratio that is used in Nature to generate growth patterns in space. Sacred Geometry studies such primal systems which reveal the unity of the cosmos by representing the relationships between numbers geometrically. The Vesica Piscis is one of the most fundamental geometrical forms of this ancient discipline and it reveals the relationship between the The Great Pyramid and the 2 dimensional expansion of a circle of one unit radius R as shown in Figure 1. This relationship is more completely described in The New View Over Atlantis by John Michell published by Thames and Hudson. Figure 1 Vesica Piscis in 2 Dimensions In the early 1970s, I became very interested in the three dimensional representation of this geometry and I visualized this as a three dimensional pyramid inside two intersecting spheres shown in Figure 2.
D&M Pyramid - Geometry
(sqrt 3)/2 = 0.866025 e/pi = 0.865256. It is this ambiguity that is resolved by the geometry of a circumscribed tetrahedron. The
http://users.starpower.net/etorun/pyramid/geometry.html

Extractions: 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.
Piguy 's Math Javascripts Page
This page has dozens of math calculators, making all sorts of math, from algebra to arithmetic to geometry, easier. Also, 50,000 decimals of pi and a logarithm table.
http://www.geocities.com/CapeCanaveral/Hall/1216/
Knowledge-Mathematic-Geometry-Pi.page
pi. What is pi? Meh, still to busy. pi = 3.1415926535897932384626433832795028841971693993751 05820974944592307816406286208998280348253421170679
http://www.geocities.com/ultrastupidneal/Knowledge-Mathematic-Geometry-Pi.html

Extractions: Unfortunately those are the first 100 digits. I can put more, when I get a little done with all my fields. I don't think I'll ever want to put more than a thousand in the history of my site, as when some of you as my site dependers really need at least that much, you will have to E-mail me at LonelyNoone@Hotmail.com . As of now, I plan on putting in to 200, or maybe 100 at a time. Well, here's the first 1,000 digits of pi, and I made it in a larger font. Q:Yo SiteMaster, your site about pi is crappy, I could easily find even more digits of pi anywhere! What? You ave the first 10, 20, 50, and even a hundred, as well as a thousand? I could easily find 2 thousand, 5,000 and even 10 thousand anywhere! Your site's last on my list!
Knowledge-Mathematic-Geometry-Pi-X.page
3. 141592653589793238462643383279502884197169399375105820974944 592307816406286208998628034825342117067982148086513282306647
http://www.geocities.com/ultrastupidneal/Knowledge-Mathematic-Geometry-Pi-X.html
Anti-Grain Geometry -
AntiGrain geometry - Version 2.1 cover_mask //-cover_full }; //-pi const double pi = 3
http://www.antigrain.com/__code/include/agg_basics.h.html

Extractions: // Anti-Grain Geometry - Version 2.1 // Permission to copy, use, modify, sell and distribute this software // This software is provided "as is" without express or implied // warranty, and with no claim as to its suitability for any purpose. // Contact: mcseem@antigrain.com // mcseemagg@yahoo.com // http://www.antigrain.com #ifndef #define namespace agg typedef signed char typedef unsigned char typedef signed short typedef unsigned short typedef signed int typedef unsigned int typedef unsigned char enum pi const double pi inline double double deg return deg pi inline double double rad return rad pi template class T struct typedef T T x1 T y1 T x2 T y2 T x1_ T y1_ T x2_ T y2_ const normalize T t if t t if t t return this bool clip const r if r r if r r if r r if r r return bool const return template class Rect Rect const Rect const Rect Rect r if r r if r r if r r if r r return r template class Rect Rect const Rect const Rect Rect r if r r if r r if r r if r r return r typedef int rect rect typedef double enum enum inline bool unsigned c return c c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c c c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline bool unsigned c return c inline unsigned unsigned c return c inline unsigned unsigned c return c inline unsigned unsigned c return c inline unsigned unsigned
Anti-Grain Geometry -
AntiGrain geometry - Version 2.1 static unsigned dimension() { return 6; } static double calc_weight(double x) { if(x 0.0) return 1.0; x *= pi; double x3
http://www.antigrain.com/__code/include/agg_image_filters.h.html

Extractions: // Anti-Grain Geometry - Version 2.1 // Permission to copy, use, modify, sell and distribute this software // This software is provided "as is" without express or implied // warranty, and with no claim as to its suitability for any purpose. // Contact: mcseem@antigrain.com // mcseemagg@yahoo.com // http://www.antigrain.com // Image transformation filters, // Filtering classes ( // Basic filter shape classes: #ifndef #define #include math h #include " agg_basics.h " namespace agg // See Implementation agg_image_filters.cpp enum class public unsigned dimension unsigned dimension const return int start const return const double const return const int const return protected void weight unsigned idx double val double unsigned idx const void normalize private const const operator const unsigned int double int template class FilterF class public public FilterF::dimension unsigned i unsigned dim dimension for i i dim i weight i i normalize private : FilterF m_filter_function class public static unsigned dimension return static double double x return x ? x
Urban Legends Reference Pages: Religion (Alabama's Slice Of Pi)
pi is merely an artifact of Euclidean geometry. Humbleys is working on a theory which he says will prove that pi is determined by the geometry of three
http://www.snopes.com/religion/pi.htm

Extractions: introduced without fanfare by Leonard Lee Lawson (R, Crossville), and rapidly gained support after a letter-writing campaign by members of the Solomon Society, a traditional values group. Governor Guy Hunt says he will sign it into law on Wednesday. The law took the state's engineering community by surprise. "It would have been nice if they had consulted with someone who actually uses pi," said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, pi is a Greek letter that signifies the ratio of the circumference of a circle to its diameter. It is often used by engineers to calculate missile trajectories. Prof. Kim Johanson, a mathematician from University of Alabama, said that pi is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that pi is an irrational number, which means that it has an infinite number of digits after the decimal point and can never be known exactly. Nevertheless, she said, pi is precisly defined by mathematics to be "3.14159, plus as many more digits as you have time to calculate". "I think that it is the mathematicians that are being irrational, and it is time for them to admit it," said Lawson. "The Bible very clearly says in
LucyTuning*LucyScaleDevelopments*LucyTuned Lullabies*Pi Tuning*John Longitude Ha
geometry is a mapping system of space. Music is a mapping system of sound and other vibrating patterns. The Ancient Greeks can not claim the discovery of pi,
http://www.lucytune.com/academic/music_and_geometry.html

Extractions: Search This Site The Web for Home New to LucyTuning? Academic & Research, John "Longitude" Harrison LucyTuned Lullabies ... info@lucytune.com MusicAsEasyAsPi - Music, Ancient Greek Ratios, Geometry and Speculations. Once upon a time some two and a half thousand years ago the Ancient Greek philosophers thought about space, time and musical sounds. Pythagoras became best know in our era for his concept that the sum of the squares of the adjacent sides of a right angle triangle are equal to the square of the hypotenuse. (a^2 + b^2 = c^2) Stated like this, some people find it difficult to visualize, but a simple drawing makes it abundantly clear. Since the original drawings were probably marked with a stick in sand my untidy proportions are comparable to the first attempts. A picture as with music, a sound is worth a million words. What does all this have to do with music? You can justifiably ask.
POV-Ray: A Tool For Creating Engaging Visualisation Of Geometry
A more interesting geometric primitive is a parametric surface, to illustrate this consider the parametric { function { cos(2*pi*u pi/2)*cos(2*pi*(-u+v)+pi/2
http://astronomy.swin.edu.au/~pbourke/povray/representation/

Extractions: January 2004 Abstract Computers are now a standard tool for creating, exploring, and presenting geometric form and mathematics. Finding the right software tools can be difficult, especially so when high quality and visually appealing images are required. This paper will discuss one particular package (POV-Ray) used with great success by the author. A general discussion of the desirable features will be presented along with examples based around the familiar tetrahedral form. Introduction The mathematician and geometer often needs to represent equations or geometry visually, both for their own insight (visualisation) and as a way of conveying information to a wider audience. There are a number of software packages that have been designed to meet this need but most concentrate on the former goal and as such may be able to create informative images for the expert but tend to be limited in their ability to create higher quality images that may be more informative and attractive to a general audience. There are a number of consideration when choosing software for any task and there are some others that are relevant to the presentation of geometry.
Themepark - Utah Education Network
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
History Of Mathematics: Egyptian Math, Pi, Magic Squares, Chinese Arithmetic, Me
the value of pi Archimedes method of exhaustion, Leibniz series, Machin formula using tangents, and others. THALES, FOUNDER OF GREEK geometry (585 BCE) The
http://nunic.nu.edu/~frosamon/history/bc3000.html
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

Extractions: 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. 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
MSN Encarta - Geometry
Archimedes, one of the greatest Greek scientists, made a number of important contributions to geometry during the 3rd century bc. See pi.
http://encarta.msn.com/encyclopedia_761569706_3/Geometry.html

Extractions: MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Tasks Find in this article Print Preview Send us feedback Related Items Mathematics Plane Geometry, geometric figures in two dimensions more... Magazines Search the Encarta Magazine Center for magazine and news articles about this topic Further Reading Editors' Picks Geometry News Search MSNBC for news about Geometry Internet Search Search Encarta about Geometry Search MSN for Web sites about Geometry Also on Encarta Encarta guide: The Reagan legacy Compare top online degrees Proud papas: Famous dads with famous kids Also on MSN Father's Day present ideas on MSN Shopping Breaking news on MSNBC Switch to MSN in 3 easy steps Our Partners Capella University: Online degrees LearnitToday: Computer courses CollegeBound Network: ReadySetGo Kaplan Test Prep and Admissions Encyclopedia Article from Encarta Advertisement Page 3 of 3 Geometry Multimedia 6 items Article Outline Introduction Methodology Euclidean Geometry Analytic Geometry ... History of Geometry D Conic Sections Conic sections are curves formed by the intersection of a plane with the surface of a cone. (When discussing conic sections
Geometry 101 Example #5
Inspection of the geometry indicates a solution between pi/4 and pi/3 where the upper bound is determined from the equation x=acos(a/2r) when a = r. The
http://home.netcom.com/~bled/geometry.html

Extractions: 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 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
B.U. Center For Polymer Studies:JAVA Applets
Our study of the geometry tells us this ratio is pi/4. So, now we can estimate pi as. pi = 4 x (Number of Darts in Circle) / (Number of Darts in Square).
http://polymer.bu.edu/java/java/montepi/MontePi.html

Extractions: Monte Pi Java Applet The Monte Carlo method is used in modeling a wide-range of physical systems at the forefront of scientific research today. Monte Carlo simulations are statistical models based on a series of random numbers. Let's consider the problem of estimating Pi by utilizing the Monte Carlo method. Suppose you have a circle inscribed in a square (as in the figure). The experiment simply consists of throwing darts on this figure completely at random (meaning that every point on the dartboard has an equal chance of being hit by the dart). How can we use this experiment to estimate Pi? The answer lies discovering the relationship between the geometry of the figure and the statistical outcome of throwing the darts. Let's first look at the geometry of the figure. Let's assume the radius of the circle is R , then the Area of the circle = Pi R and the Area of the square = 4 R Now if we divide the area of the circle by the area of the square we get Pi / 4 But, how do we estimate Pi by simulation? In the simulation, you keep throwing darts at random onto the dartboard. All of the darts fall within the square, but not all of them fall within the circle. Here's the key. If you throw darts completely at random, this experiment estimate the ratio of the area of the circle to the area of the square, by counting the number of darts in each. Our study of the geometry tells us this ratio is Pi/4 . So, now we can estimate Pi as
Geometry Question
Re geometry question Posted Tuesday, May 11, 2004 759 PM (CST y = (float)Math.Cos(xRot * Math.pi / 180.0f) * y (float)Math.Sin(xRot * Math.pi / 180.0f) * z
http://www.randyridge.com/Tao/Discussions/Help/1776.aspx

Extractions: Posted: Tuesday, May 11, 2004 2:57 AM (CST) Hallo, my problem is not directly TAO related, and furthermore this may be a rather stupid question. But I'm stuck for some time now and I hope someone can give me a clue with this. What I want to do is transforming some coordinates into the current OpenGL coordinate system ("by hand"). The situation is something like this. I have done some rotations and transformations like Gl.glRotatef(fXRot, 1.0f, 0.0f, 0.0f);
Easy As Pi
EASY AS pi. Three wonderful things happen when you use literature to enhance your existing mathematics program. Back to Ideas. geometry.
http://www.todaysteacher.com/EasyAsPi.htm

Extractions: EASY AS Pi Three wonderful things happen when you use literature to enhance your existing mathematics program. One, curiosity is generated from the literature being used. Two, the literature creates questions that propel your students mathematical understandings. Three, students develop a relationship between the real world and mathematics through the literature. Children of all ages, yes, even in middle school, love to be read to. Use this to your advantage and start spicing up your math lessons. Literature Ideas COUNTING Patterns and Functions Estimation / Comparison Measurement ... Money COUNTING The Twelve Circus Rings , Seymour Chwast - Students count the performers in the circus as it is read. Have students write their own versions of the story, which follows the rhythm of The Twelve Days of Christmas. The Hundred Penny Box , Sharon Bell Mathis - Students can count, measure, and weigh pennies. Write Penny Autobiographies writing a paragraph about each year of their life on a penny shaped piece of paper, creating a book shaped like a penny.
Comp.Graphics.Algorithms FAQ, Section 6
Ti not incident to pi. The areas of these triangles Ti are proportional to the barycentric coordinates ti of p. Reference Coxeter, Intro. to geometry, p.217
http://exaflop.org/docs/cgafaq/cga6.html

Extractions: Frequently Asked Questions Section 6. Geometric Structures and Mathematics (C) 1998 Joseph O'Rourke. Subject 6.01: Where can I get source for Voronoi/Delaunay triangulation? For 2-d Delaunay triangulation, try Shewchuk's triangle program. It includes options for constrained triangulation and quality mesh generation. It uses exact arithmetic. The Delaunay triangulation is equivalent to computing the convex hull of the points lifted to a paraboloid. For n-d Delaunay triangulation try Clarkson's hull program (exact arithmetic) or Barber and Huhdanpaa's Qhull program (floating point arithmetic). The hull program also computes Voronoi volumes and alpha shapes. The Qhull program also computes 2-d Voronoi diagrams and n-d Voronoi vertices. The output of both programs may be visualized with Geomview. There are many other codes for Delaunay triangulation and Voronoi diagrams. See Amenta's list of computational geometry software. The Delaunay triangulation satisfies the following property: the circumcircle of each triangle is empty. The Voronoi diagram is the closest-point map, i.e., each Voronoi cell identifies the points that are closest to an input site. The Voronoi diagram is the dual of the Delaunay triangulation. Both structures are defined for general dimension. Delaunay triangulation is an important part of mesh generation.
Efg's Reference Library: Delphi Graphics Algorithms -- Math/Geometry
angle = 180 * (1 + ArcTan2(jTextjTarget, iTarget-iText) / pi); IF angle = 360.0 THEN angle = angle - 360.0;. geometry, geometry Library, geometry.ZIP.
http://homepages.borland.com/efg2lab/Library/Delphi/Graphics/Math.htm

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