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Excel offers many user interface tweaks over the earliest electronic spreadsheets; however, the essence remains the same as in the original spreadsheet software, VisiCalc: the program displays cells organized in rows and columns, and each cell may contain data or a formula, with relative or absolute references to other cells.
A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
Likewise, instead of using a named range of cells, a range reference can be used. Reference to a range of cells is typical of the form (A1:A6), which specifies all the cells in the range A1 through to A6. A formula such as "=SUM(A1:A6)" would add all the cells specified and put the result in the cell containing the formula itself.
Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written as the sum of three fourth powers, but 200 years later, in 1986, this was disproven by Elkies with: 20615673 4 = 18796760 4 ...
The difference of two squares can also be used as an arithmetical short cut. If two numbers (whose average is a number which is easily squared) are multiplied, the difference of two squares can be used to give you the product of the original two numbers. For example: = (+)
LibreOffice Calc is the spreadsheet component of the LibreOffice software package. [6] [7]After forking from OpenOffice.org in 2010, LibreOffice Calc underwent a massive re-work of external reference handling to fix many defects in formula calculations involving external references, and to boost data caching performance, especially when referencing large data ranges.
The Cartesian product, S × T, of two well-ordered sets S and T can be well-ordered by a variant of lexicographical order that puts the least significant position first. Effectively, each element of T is replaced by a disjoint copy of S. The order-type of the Cartesian product is the ordinal that results from multiplying the order-types of S and T.
The squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates; Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares) The British flag theorem for rectangles equates two sums of two squares