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The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. [1]
Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC [1] in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula.
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
Also, programs can be written that pull information from the worksheet, perform some calculations, and report the results back to the worksheet. In the figure, the name sq is user-assigned, and the function sq is introduced using the Visual Basic editor supplied with Excel. Name Manager displays the spreadsheet definitions of named variables x & y.
In graph-theoretic terms, the theorem states that for a loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
Food coloring, color additive or colorant is any dye, pigment, or substance that imparts color when it is added to food or beverages. Colorants can be supplied as liquids, powders, gels, or pastes. Food coloring is commonly used in commercial products and in domestic cooking. It is not toxic.