It is derived from the Greek words gaia (geo) and metria (meter) and means earth measures.
Geometric Meaning of the Geometric Mean. The geometric mean of two positive numbers a and b is the (positive) number g whose square equals the product ab : g ² = ab. While it is possible to (at least partially) adapt the definition to handle negative numbers, I do not believe this is ever done. The length of the common tangent of two circles of diameters a and b that are tangent externally is the geometric mean of the diameters: The geometric mean appeared as a tangent to a circle in John Wallis' very first geometric interpretation of complex numbers: HL-usually in upper case-stands for Hypotenuse-Leg. It is a specialized triangle congruence theorem, the regular ones are SSS, SAS, and ASA. HL says that in two righ … t triangles, if the hypoteneuses and a pair of legs (the sides forming the right angle) are congruent, then the triangles are congruent. In any case there is some sort of geometry to all chemical compounds in a sub-microscopic sort of way, and these geometric differences can often make considerable differences in the physical and chemical properties of otherwise similar or nearly identical substances. The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers, the geometric mean is defined as. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is. The geometric mean of a data set is given by: The geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal. DEFINITION of 'Geometric Mean'. The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. Technically defined as the 'n'th root product of 'n' numbers, the formula for calculating geometric mean is most easily written as: The geometric mean is NOT the arithmetic mean and it is NOT a simple average. It is the nth root of the product of n numbers. That means you multiply a bunch of numbers together, and then take the nth root, where n is the number of values you just multiplied.  The Geometric Mean. In this video, I show how to find the geometric mean of two numbers and show what that number means in relation to the numbers that you started with. 1  Education. 2  Standard YouTube License.  Nouns denoting cognitive processes and contents. Hypernyms (geometry is a kind of...): pure mathematics (the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness). The word Geometry is derived from the Greek words gaia (geo) and metria (meter) and means earth measures. Geometry has been widely used in the field of science, engineering, computers, and art. Its origin was during the ancient civilization in Egypt, where geometry was used in their arts, astronomy, and architecture. In any case there is some sort of geometry to all chemical compounds in a sub-microscopic sort of way, and these geometric differences can often make considerable differences in the physical and chemical properties of otherwise similar or nearly identical substances.
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what does geometry mean