uncleflo
Registered since September 28th, 2017
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Tag selected: mathematics.
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Sass: Variables
Saved by uncleflo on July 10th, 2019.
Sass variables are simple: you assign a value to a name that begins with $, and then you can refer to that name instead of the value itself. But despite their simplicity, they're one of the most useful tools Sass brings to the table. Variables make it possible to reduce repetition, do complex math, configure libraries, and much more. A variable declaration looks a lot like a property declaration: it’s written <variable>: <expression>. Unlike a property, which can only be declared in a style rule or at-rule, variables can be declared anywhere you want. To use a variable, just include it in a value.
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Displacement-Length Ratio of a Yacht: Skipper's Basics – no-frills-sailing.com
Saved by uncleflo on February 24th, 2019.
When sailors are talking about their boats they often refer to ratios and numbers. That´s a tendency in human behaviour to try to generalize things to make them comparable. Of course, everybody knows that you cannot really describe apple to pears and so it´s worthless to describe a let´s say Seventies IOR-era King´s Cruiser 33 like mine to a modern day cruising yacht but we nevertheless tend to do so. The Displacement-Length-Ratio in general is a non-dimensional number. It sets into relation the displacement of a boat (expressed in pounds) to the length of her waterline (in feet). So, in general, this ratio is looking for the relation between the (heavy?) volume of water being pushed aside by a boat´s hull and the length (and therefore speed potential see for my article Hull speed vs. Froude number here) of her hull. Sounds fair enough?
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Gothic Window - How to design a full gothic window with sections
Saved by uncleflo on November 29th, 2018.
Gothic Window in Malbork Castle, Poland. How to design a gothic window with sections and colored glasses from one building in Poland. A step by step guide on how to do the Mathematics and designs to get to the finished result. Very nice for an engineer or other exterior designer.
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More Meaningful Typography
Saved by uncleflo on April 20th, 2018.
We have all heard of the golden mean (also known as the golden ratio or golden section): the self-replicating page with a proportion of 1:1.618 that is said to be found in everything from the design of ancient Greek architecture to the growth patterns of plants. This and other meaningful ratios rooted in geometry, music, nature, and history can be expressed as modular scales and put to work on the web. A modular scale is a sequence of numbers that relate to one another in a meaningful way. Using the golden ratio, for example, we can produce values for a modular scale by multiplying by 1.618 to arrive at the next highest number, or dividing by 1.618 to arrive at the next number down.
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State-space representation
Saved by uncleflo on June 23rd, 2017.
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a vector within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form. The state-space method is characterized by significant algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it. The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With {\displaystyle p} p inputs and {\displaystyle q} q outputs, we would otherwise have to write down {\displaystyle q\times p} q\times p Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions.
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Learn about Robot Inverse Kinematics
Saved by uncleflo on June 13th, 2015.
We've seen the forward kinematics problem. The inverse kinematics problem is much more interesting and its solution is more useful. At the position level, the problem is stated as, "Given the desired position of the robot's hand, what must be the angles at all of the robots joints?" Humans solve this problem all the time without even thinking about it. When you are eating your cereal in the morning you just reach out and grab your spoon. You don't think, "my shoulder needs to do this, my elbow needs to do that, etc." Below we will look at how most robots have to solve the problem. We will start with a very simple example.
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Online Algebra Calculator | Maxima-online
Saved by uncleflo on April 2nd, 2015.
Calculate the Jacobian from a website, very powerful. Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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Calculating reflected ray
Saved by uncleflo on February 22nd, 2015.
This short note gives the equation for a reflected ray as used in many computer rendering applications, eg: ray tracing. Given a ray Ri incident at a point on a surface with normal N one wishes to determine the reflected ray from that point. The geometry and nomenclature is given in the following diagram.
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graphics.stanford.edu/courses/cs148-10-summer/docs/2006--degreve--reflection_refraction.pdf
Saved by uncleflo on February 22nd, 2015.
When writing a ray tracer, sooner or later you’ll stumble on the problem of reflection and transmission. To visualize mirror-like objects, you need to reflect your viewing rays. To simulate a lens, you need refraction. While most people have heard of the law of reflection and Snell’s law, they often have difficulties with actually calculating the direction vectors of the reflected and refracted rays. In the following pages, exactly this problem will be addressed. As a bonus, some Fresnel equations will be added to the mix, so you can actually calculate how much light is reflected or transmitted (yes, it’s possible). At the end, you’ll have some usable formulas to use in your latest ray tracer.
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Calculating the Eigenvalue and Eigenvector of a Matrix on the TI-89 Family, TI-92 Plus, and Voyage™ 200 Graphing Calculators. - Knowledge Base by Texas Instruments - US and Canada
Saved by uncleflo on January 20th, 2015.
How do I calculate the eigenvalue and eigenvector of a matrix on the TI-89 family, TI-92 Plus, and Voyage 200 graphing calculators? To calculate the eigenvalue and eigenvector of a matrix on the TI-89 family, TI-92 Plus, and Voyage 200 refer to the instructions below
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OpenGL Mathematics
Saved by uncleflo on December 7th, 2014.
OpenGL Mathematics (GLM) is a header only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specification and released under the MIT license. This library provides classes and functions designed and implemented following as strictly as possible the GLSL conventions and functionalities so that when a programmer knows GLSL, he knows GLM as well, making it really easy to use. This project isn't limited to GLSL features. An extension system provides extended capabilities: matrix transformations, quaternions, half-based types, random number generation, procedural noise functions, etc.
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The Engineering Toolbox - Area Moment of Inertia
Saved by uncleflo on September 2nd, 2014.
Resources, Tools and Basic Information for Engineering and Design of Technical Applications! This great website is a great lookup site for formulas and calculations used in the engineering world. Second Moment of Area or Area Moment of Inertia. Moment of Inertia of an Area, Area Moment of Inertia, also known as Second Moment of Area - I, is a property of shape that is used to predict deflection, bending and stress in beams.
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[GUIDE] Using LaTeX on the forums
Saved by uncleflo on September 2nd, 2014.
On this course, you will be using a lot of maths. Sometimes, you may need clarification on how to use maths for a particular problem. Luckily, you can use LaTeX on the forums to display maths in a readable format (as opposed to unwieldy formats like 4*10^6 which can be difficult to parse). There are a lot of different commands for LaTeX, but you will only need a few in this course. To start using LaTeX, you first need to type $$ - this is telling the forums software that whatever you type in between the dollar signs is LaTeX and should be displayed as LaTeX
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Jiskha Homework Help
Saved by uncleflo on September 2nd, 2014.
Welcome to Jiskha Homework Help! Post homework questions online and get free homework help from tutors. More than 200 tutors volunteer their time to help over 4,000 students with homework everyday. Students receive answers from teachers in various school subjects including math, science, social studies and more.
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An Intuitive (and Short) Explanation of Bayes’ Theorem | BetterExplained
Saved by uncleflo on July 16th, 2014.
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like myself:
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MathJax
Saved by uncleflo on June 3rd, 2014.
MathJax is an open source JavaScript display engine for mathematics that works in all browsers. No more setup for readers. No more browser plugins. No more font installations… It just works.
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True, Reactive, and Apparent power : Power Factor
Saved by uncleflo on February 23rd, 2014.
We know that reactive loads such as inductors and capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they actually do dissipate power. This “phantom power” is called reactive power, and it is measured in a unit called Volt-Amps-Reactive (VAR), rather than watts. The mathematical symbol for reactive power is (unfortunately) the capital letter Q. The actual amount of power being used, or dissipated, in a circuit is called true power, and it is measured in watts (symbolized by the capital letter P, as always). The combination of reactive power and true power is called apparent power, and it is the product of a circuit's voltage and current, without reference to phase angle. Apparent power is measured in the unit of Volt-Amps (VA) and is symbolized by the capital letter S.
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Magnitude & Phase - Minimum Phase
Saved by uncleflo on February 8th, 2014.
Ah yes, magnitude and phase. You probably never actually have to bother calculating them explicitly now, seeing as Matlab and Octave will do it for you.
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SolidWorks Simulation
Saved by uncleflo on November 24th, 2011.
Powerful design validation packages directly within SolidWorks. Solid Solutions provides design validation tools so you can go beyond hand calculations by verifying your intuitions and study the real-world performance of different design alternatives without ever leaving the design environment
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Robotics and automation handbook - Thomas R. Kurfess - Google Books
Saved by uncleflo on November 24th, 2011.
The history of robotics is one that is highlighted by a fantasy world that has provided the inspiration to convert fantasy into reality. It is a history rich with cinematic creativity, scientific ingenuity, and entrepreneurial vision. Quite surprisingly, the definition of a robot is controversial, even among roboticists. At one end of the spectrum is the science fiction version of a robot, typically one of a human form - and android or humanoid - with anthropomorphic features. At the oher end of the spectrum is the repetitive, efficient robot of industrial automation.
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Example: Solving a first order ODE by Laplace transforms
Saved by uncleflo on October 31st, 2011.
I have a audiovisual digital lecture on YouTube that shows the use of Euler’s method to solve a first order ordinary differential equation (ODE). To show the accuracy of Euler’s method, I compare the approximate answer to the exact answer. A YouTube viewer asked me: How did I get the exact answer? In this blog, I use the Laplace transform technique to find the exact answer to the ODE. In a previous blog, I showed how to find the exact answer to the ODE by the classicial solution technique.
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Mod- 9 Lec-22 Stability of Equilibrium
Saved by uncleflo on October 30th, 2011.
Lecture Series on Engineering Mechanics by Dr.G.Saravana Kumar, Department of Mechanical Engineering, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in
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How to Build a Robot Tutorial - Society of Robots#end_effector#end_effector
Saved by uncleflo on May 11th, 2008.
Society of Robots, Robot arm tutorial
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