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LiveMath uses a worksheet-based approach, similar to products like Mathematica or MathCAD. The user enters equations into the worksheet and then uses the built-in functions to help solve them, or reduce them numerically. Workbooks typically contain a number of equations separated into sections, along with data tables, graphs, and similar outputs.
A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y.
Specifically, draw a diagonal line connecting two points on the diagram so that every other point is either on or to the right and above it. There is at least one such line if the curve passes through the origin. Let the equation of the line be qα+pβ=r. Suppose the curve is approximated by y=Cx p/q near the origin.
The nested triangles graph requires this much area no matter how it is embedded, [2] and several methods are known that can draw planar graphs with at most quadratic area. [3] [4] Binary trees, and trees of bounded degree more generally, have drawings with linear or near-linear area, depending on the drawing style.
In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations. [1]
Yes (print as PDF) Yes No Web Free. Registration needed only to share worksheets. PDF No IguanaTex: No Yes No Yes Yes No No No Free PowerPoint plugin for inserting LaTeX equations iMathEQ editor: Yes Yes No Yes Yes Yes No No Web (Win, Mac, iOS, Android)
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