The need for communications between tasks depends upon your problem: Some types of problems can be decomposed and executed in parallel with virtually no need for tasks to share data. These types of problems are often called embarrassingly parallel - little or no communications are required. For example, imagine an image processing operation where every pixel in a black and white image needs to have its color reversed.
To avoid this vicious circle certain concepts must be taken as primitive concepts; terms which are given no definition. When the line concept is a primitive, the behaviour and properties of lines are dictated by the axioms which they must satisfy.
In a non-axiomatic or simplified axiomatic treatment of geometry, the concept of a primitive notion may be too abstract to be dealt with.
In this circumstance it is possible that a description or mental image of a primitive notion is provided to give a foundation to build the notion on which would formally be based on the unstated axioms.
Descriptions of this type may be referred to, by some authors, as definitions in this informal style of presentation. These are not true definitions and could not be used in formal proofs of statements.
In Euclidean geometry[ edit ] See also: Euclidean geometry When geometry was first formalised by Euclid in the Elementshe defined a general line straight or curved to be "breadthless length" with a straight line being a line "which lies evenly with the points on itself".
In fact, Euclid did not use these definitions in this work and probably included them just to make it clear to the reader what was being discussed.
In modern geometry, a line is simply taken as an undefined object with properties given by axioms but is sometimes defined as a set of points obeying a linear relationship when some other fundamental concept is left undefined.
For example, for any two distinct points, there is a unique line containing them, and any two distinct lines intersect in at most one point. In higher dimensions, two lines that do not intersect are parallel if they are contained in a planeor skew if they are not. Any collection of finitely many lines partitions the plane into convex polygons possibly unbounded ; this partition is known as an arrangement of lines.
On the Cartesian plane[ edit ] Lines in a Cartesian plane or, more generally, in affine coordinatescan be described algebraically by linear equations. In two dimensionsthe equation for non-vertical lines is often given in the slope-intercept form:We'll write the general form of the quadratic: ax^2 + bx + c = y.
If the graph passes through the given points, that means that the coordinates of the points verify the equation of the quadratic.
Write an equation in slope-intercept form of the line with slope, m = -2 and y-intercept, b = 8/5 y=-2x+8/5 Find the slope of the line that passes through the points (0,-1) and (2,3).
Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if.
It's called the point-slope formula (Duh!) You are going to use this a LOT! Luckily, it's pretty easy -- let's just do one: Let's find the equation of the line that passes through the point. The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry - Kindle edition by Mario Livio.
Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry.
This is the first tutorial in the "Livermore Computing Getting Started" workshop.
The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry - Kindle edition by Mario Livio. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry. Graphing straight lines. Using the equation to sketch the line. If you are given an equation of a straight line and asked to draw its graph all you need to do is find two points whose coordinates satisfy the equation and plot the points. § Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted (a) The provisions of §§ of this subchapter shall be .
It is intended to provide only a very quick overview of the extensive and broad topic of Parallel Computing, as a lead-in for the tutorials that follow it.