1915-16.] the " Geometria Organica" of Colin Maclaurin. 87 V.—-The
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Mathematical Documentation of the objects realized in the visualization program 3D-XplorMath Select the Table Of Contents (TOC) of the desired kind of objects: Table Of Contents of Planar Curves Table Of Contents of Space Curves Surface Organisation Go To Platonics Table of Contents of Conformal Maps Table Of Contents of Fractals ODEs Table Of Contents of Lattice Models Table Of Contents of Soliton Traveling Waves Shepard Tones Homepage of 3D-XPlorMath (3DXM): http://3d-xplormath.org/ Tutorial movies for using 3DXM: http://3d-xplormath.org/Movies/index.html Version November 29, 2020 The Surfaces Are Organized According To their Construction Surfaces may appear under several headings: The Catenoid is an explicitly parametrized, minimal sur- face of revolution. Go To Page 1 Curvature Properties of Surfaces Surfaces of Revolution The Unduloid, a Surface of Constant Mean Curvature Sphere, with Stereographic and Archimedes' Projections TOC of Explicitly Parametrized and Implicit Surfaces Menu of Nonorientable Surfaces in previous collection Menu of Implicit Surfaces in previous collection TOC of Spherical Surfaces (K = 1) TOC of Pseudospherical Surfaces (K = −1) TOC of Minimal Surfaces (H = 0) Ward Solitons Anand-Ward Solitons Voxel Clouds of Electron Densities of Hydrogen Go To Page 1 Planar Curves Go To Page 1 (Click the Names) Circle Ellipse Parabola Hyperbola Conic Sections Kepler Orbits, explaining 1=r-Potential Nephroid of Freeth Sine Curve Pendulum ODE Function Lissajous Plane Curve Catenary Convex Curves from Support Function Tractrix -
A Handbook on Curves and Their Properties
SEELEY G. 1 1UDD LIBRARY LAWRENCE UNIVERSITY Appleton, Wisconsin «__ CURVES AND THEIR PROPERTIES A HANDBOOK ON CURVES AND THEIR PROPERTIES ROBERT C. YATES United States Military Academy J. W. EDWARDS — ANN ARBOR — 1947 97226 NOTATION octangular C olar Coordin =r.t^r ini Tangent and the Rad ,- ^lem a Copyright 1947 by R m Origin to Tangent. i i = /I. f(s ) = C well Intrinsic Egua 9 ;(f «r,p) = C 1- Lithoprinted by E rlll CONTENTS PREFACE nephroid and teacher lume proposes to supply to student curves. Rather ,n properties of plane Pedal Curves e Pedal Equations U vhi C h might be found ^ Yc 31 r , 'f Lr!-ormation and in engine useful in the classroom 3 aid in the s Radial Curves alphabetical arrangement is Roulettes Semi-Cubic Parabola Sketching Evolutes, Curve Sketching, and Spirals Strophoid If 1 :s readily understandable. Trigonometric Functions .... Trochoids Witch of Agnesi bfi Stropho: i including the Astroid, HISTORY: The Cycloidal curves, discovered by Roemer (1674) In his search for the Space Is provided occasionally for the reader to ir ;,„ r e for gear teeth. Double generation was first sert notes, proofs, and references of his own and thus be st form noticed by Daniel Bernoulli in 1725- It is with pleasure that the author acknowledges a hypo loid o f f ur valuable assistance in the composition of this work. 1. DESCRIPTION: The d is y Mr. H. T. Guard criticized the manuscript and offered Le roll helpful suggestions; Mr. Charles Roth and Mr. William radius four Lmes as la ge- -oiling upon the ins fixed circle (See Epicycloids) ASTROID EQUATIONS: = cos 1 1 1 (f)(3 x + - a y sin [::::::: = (f)(3 :ion: (Fig. -
The Cissoid of Diocles
Playing With Dynamic Geometry by Donald A. Cole Copyright © 2010 by Donald A. Cole All rights reserved. Cover Design: A three-dimensional image of the curve known as the Lemniscate of Bernoulli and its graph (see Chapter 15). TABLE OF CONTENTS Preface.................................................................................................................. xix Chapter 1 – Background ............................................................ 1-1 1.1 Introduction ............................................................................................................ 1-1 1.2 Equations and Graph .............................................................................................. 1-1 1.3 Analytical and Physical Properties ........................................................................ 1-4 1.3.1 Derivatives of the Curve ................................................................................. 1-4 1.3.2 Metric Properties of the Curve ........................................................................ 1-4 1.3.3 Curvature......................................................................................................... 1-6 1.3.4 Angles ............................................................................................................. 1-6 1.4 Geometric Properties ............................................................................................. 1-7 1.5 Types of Derived Curves ....................................................................................... 1-7 1.5.1 Evolute -
Bundle Block Adjustment with 3D Natural Cubic Splines
BUNDLE BLOCK ADJUSTMENT WITH 3D NATURAL CUBIC SPLINES DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Won Hee Lee, B.S., M.S. ***** The Ohio State University 2008 Dissertation Committee: Approved by Prof. Anton F. Schenk, Adviser Prof. Alper Yilmaz, Co-Adviser Adviser Prof. Ralph von Frese Graduate Program in Geodetic Science & Surveying c Copyright by Won Hee Lee 2008 ABSTRACT One of the major tasks in digital photogrammetry is to determine the orienta- tion parameters of aerial imageries correctly and quickly, which involves two primary steps of interior orientation and exterior orientation. Interior orientation defines a transformation to a 3D image coordinate system with respect to the camera’s per- spective center, while a pixel coordinate system is the reference system for a digital image, using the geometric relationship between the photo coordinate system and the instrument coordinate system. While the aerial photography provides the interior orientation parameters, the problem is reduced to determine the exterior orientation with respect to the object coordinate system. Exterior orientation establishes the position of the camera projection center in the ground coordinate system and three rotation angles of the camera axis to represent the transformation between the image and the object coordinate system. Exterior orientation parameters (EOPs) of the stereo model consisting of two aerial imageries can be obtained using relative and absolute orientation. EOPs of multiple overlapping aerial imageries can be computed using bundle block adjustment. Bundle block adjustment reduces the cost of field surveying in difficult areas and verifies the accuracy of field surveying during the process of bundle block adjustment. -
MF-$0.75 HC Not Available from EDRS. PLUS POSTAGE Geometry
DOCUMENT RESUME ED 100 648 SE 018 119 AUTHOR Yates, Robert C. TITLE Curves and Their Properties. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C. PUB DATE 74 NOTE 259p.; Classics in Mathematics Education, Volume 4 AVAILABLE FROM National Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, Virginia 22091 ($6.40) EDRS PRICE MF-$0.75 HC Not Available from EDRS. PLUS POSTAGE DESCRIPTORS Analytic Geometry; *College Mathematics; Geometric Concepts; *Geometry; *Graphs; Instruction; Mathematical Enrichment; Mathematics Education;Plane Geometry; *Secondary School Mathematics IDENTIFIERS *Curves ABSTRACT This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch orsketches, a description of the curve, a a icussion of pertinent facts,and a bibliography. Depending upon the curve, the discussion may cover defining equations, relationships with other curves(identities, derivatives, integrals), series representations, metricalproperties, properties of tangents and normals, applicationsof the curve in physical or statistical sciences, and other relevantinformation. The curves described range from thefamiliar conic sections and trigonometric functions through tit's less well knownDeltoid, Kieroid and Witch of Agnesi. Curve related - systemsdescribed include envelopes, evolutes and pedal curves. A section on curvesketching in the coordinate plane is included. (SD) U S DEPARTMENT OFHEALTH. EDUCATION II WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCuME N1 ITASOLE.* REPRO MAE° EXACTLY ASRECEIVED F ROM THE PERSON ORORGANI/AlICIN ORIGIN ATING 11 POINTS OF VIEWOH OPINIONS STATED DO NOT NECESSARILYREPRE INSTITUTE OF SENT OFFICIAL NATIONAL EDUCATION POSITION ORPOLICY $1 loor oiltyi.4410,0 kom niAttintitd.: t .111/11.061 . -
2Dcurves in .Pdf Format (1882 Kb) Curve Literature Last Update: 2003−06−14 Higher Last Updated: Lennard−Jones 2002−03−25 Potential
2d curves A collection of 631 named two−dimensional curves algebraic curves are a polynomial in x other curves and y kid curve line (1st degree) 3d curve conic (2nd) cubic (3rd) derived curves quartic (4th) sextic (6th) barycentric octic (8th) caustic other (otherth) cissoid conchoid transcendental curves curvature discrete cyclic exponential derivative fractal envelope gamma & related hyperbolism isochronous inverse power isoptic power exponential parallel spiral pedal trigonometric pursuit reflecting wall roulette strophoid tractrix Some programs to draw your own For isoptic cubics: curves: • Isoptikon (866 kB) from the • GraphEq (2.2 MB) from University of Crete Pedagoguery Software • GraphSight (696 kB) from Cradlefields ($19 to register) 2dcurves in .pdf format (1882 kB) curve literature last update: 2003−06−14 higher last updated: Lennard−Jones 2002−03−25 potential Atoms of an inert gas are in equilibrium with each other by means of an attracting van der Waals force and a repelling forces as result of overlapping electron orbits. These two forces together give the so−called Lennard−Jones potential, which is in fact a curve of thirteenth degree. backgrounds main last updated: 2002−11−16 history I collected curves when I was a young boy. Then, the papers rested in a box for decades. But when I found them, I picked the collection up again, some years spending much work on it, some years less. questions I have been thinking a long time about two questions: 1. what is the unity of curve? Stated differently as: when is a curve different from another one? 2. which equation belongs to a curve? 1. -
On Some Osculating Figures of the Plane Curve, by Kazuhiko MAEDA(Formerly Jusaku MAEDA),Seudai
On some Osculating Figures of the Plane Curve, by Kazuhiko MAEDA(formerly Jusaku MAEDA),Seudai. 1. The parabola of index n. e shall call the curve represented by W where x and y are rectangular coordinates of a point, a parabola of index n, n being a given number positive or negative. When n is positive, the origin is a point on the curve and the tangent at this point is the x-axis or y-axis according as n is greater or less than unity. When n is negative, the origin is no longer a point on the curve, and the x-axis is an asymptote of the curve. In all cases, the origin and the x-axis have special relation to the curve. And we shall call, for the sake of convenience, the origin the initial point, while the x-axis the initial line of the curve. The parabola of index n (1.1) may be represented parametrically by (1.2) where z is the Gaussian coordinate of a point on the curve and ƒÉ a real parameter. In general, the parabola of index n can be re- presented by where ƒÄ is any point on the curve, w the initial point of the curve, a complex constant, distinct from zero and ƒÉ a real parameter. ƒ¿ Let us denote by (M) a given curve and by M an ordinary point on this curve. Let s be the arc length of (M) measured from a certain fixed point on (M) to M, and k and p be respectively the, curvature and the radius of curvature of (M) at M If we denote by z the Gauesian coordinate of the point M, we have the fundamental equation of the curve (M) as follows: (1.4), where accents denote differentiation with respect to s. -
Hilton, Plane Algebraic Curves
Cornell ftntuetgUg Babrarg Strata, SJem 5«>*h BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND THE GIFT OF HENRY W. SAGE 1891 ( Cornell University Library QA 565.H65 Plane algebraic curves, 3 1924 001 544 216 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924001544216 PLANE ALGEBRAIC CURVES OXFOKD UNIVEESITY PEESS LONDON EDINBURGH GLASGOW NEW YORK TOEONTO MELBOURNE CAPE TOWN BOMBAY HUMPHREY MILFORD PUBLISHER TO THE UNIVERSITY PLANE ALGEBRAIC CURVES BY HAROLD HILTON, M.A., D.Sc. PROFESSOR Or MATHEMATICS IN THE UNIVERSITY OF LONDON AND HEAD OF THE MATHEMATICAL DEPARTMENT OF BEDFORD COLLEGE FORMERLY FELLOW OF MAGDALEN COLLEGE, OXFORD, AND ASSISTANT MATHEMATICAL LECTURER AT THE UNIVERSITY COLLEGE, BANGOR OXFORD AT THE CLARENDON PRESS 1920 PEEFACE THOUGH the theory of plane algebraic curves still attracts mathematical students, the English reader has not many suitable books at his disposal. Salmon's classic treatise supplied all that could be desired at the time of its appearance, but the last edition was published some forty years ago, and has been long out of print. It seemed therefore as if a new book on the subject might be useful, if only to bring some more recent developments within reach of the student. In the preparation of this volume I have made frequent use of the books written by Salmon, Basset, Wieleitner, Teixeira, Loria, &c. But most of the con- tents and examples are extracted from a very large number of mathematical periodicals.