National Air and Space Museum: How Things Fly. Point-Line Distance. Let a line in three dimensions be specified by two points and lying on it, so a vector along the line is given by The squared distance between a point on the line with parameter and a point is therefore To minimize the distance, set and solve for to obtain where denotes the dot product.
Back into (2) to obtain Using the vector quadruple product denotes the cross product then gives and taking the square root results in the beautiful formula Here, the numerator is simply twice the area of the triangle formed by points , and , and the denominator is the length of one of the bases of the triangle, which follows since, from the usual triangle area formula, Weierstrass functions. Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere".
Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent. It is also an example of a fourier series, a very important and fun type of series. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x.
Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr. Professor Michael Accorsi: Parachute Simulations. What Every Computer Scientist Should Know About Floating-Point Arithmetic. This appendix is an edited reprint of the paper , by David Goldberg, published in the March, 1991 issue of Computing Surveys.
Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission. Abstract Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising because floating-point is ubiquitous in computer systems. Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. Categories and Subject Descriptors: (Primary) C.0 [Computer Systems Organization]: General -- ; D.3.4 [Programming Languages]: Processors -- ; G.1.0 [Numerical Analysis]: General -- (Secondary) General Terms: Algorithms, Design, Languages Introduction Rounding Error.
CGNS Standard Interface Data Structures - Conventions. (CGNS Documentation Home Page) (Steering Committee Charter) (Overview and Entry-Level Document) (A User's Guide to CGNS) () (SIDS-to-ADF File Mapping Manual) (SIDS-to-HDF File Mapping Manual) (Mid-Level Library) (ADF User's Guide) (CGNS Tools and Utilities) (Introduction) (Design Philosophy of Standard Interface Data Structures) () (Building-Block Structure Definitions) (Data-Array Structure Definitions) (Hierarchical Structures) (Grid Coordinates, Elements, and Flow Solution) (Multizone Interface Connectivity) (Boundary Conditions) (Governing Flow Equations) (Time-Dependent Flow) (Miscellaneous Data Structures) (Conventions for Data-Name Identifiers) (Structured Two-Zone Flat Plate Example) Data Structure Notation Conventions The intellectual content of the CGNS database is defined in terms of C-like notation including typedefs and structures.
The database is made up of entities, and each entity has a type associated with it. [Mathematica 3.0, Wolfram Research, Inc. Pet_t MyFavoritePet ; CGNS Standard Interface Data Structures - Conventions. List of geometry topics. From Wikipedia, the free encyclopedia This is a list of geometry topics, by Wikipedia page.
Geometric shape covers standard terms for plane shapes Types, methodologies, and terminologies of geometry Euclidean geometry, foundations Euclidean plane geometry List of computer graphics and descriptive geometry topics. Log In - Computational Science - Stack Exchange. Department of Electrical and Computer Engineering. Douglas Wilhelm Harder, M.Math.
University of Waterloo Department of Electrical and Computer Engineering and Richard Khoury, Ph.D. Lakehead University Department of Software Engineering This represents many years of work on preparing a free on-line text book for numerical analysis specifically targeting electrical and computer engineering.