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Q:A:### Quick Answer

**A geometric constraint is a limitation placed on an object, which can have two dimensions or more, because there are zero degrees of freedom.** An object that is fully constrained cannot be geometrically altered; in other words, its angles and side lengths and positions cannot be changed unless the specification of one of the existing dimensions is altered first.

Geometric constraints are imposed by designating a side length or angle to be a certain value. For example, if two angles of a triangle are specified as 45 and 90 degrees, the third angle is constrained to being 45 degrees. In order to change that third angle, one of the first two angles would have to be changed first.

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## What are some arithmetic and geometric formulas?

A:Arithmetic formulas originate from the need to determine the value or position of a specific term within an arithmetic sequence, where the difference between successive terms is a constant d, such as "an = a1 - (n - 1)d." Geometric formulas are derived from a similar need but applied to a geometric sequence with a common ratio of r, such as "an = a1 * r^(n - 1)."

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## What is geometric probability?

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Full Answer >**Geometric probability is a concept that involves the distributions of volume, area and length for objects under very specific conditions.**The basic concept is the same as that behind normal probability, but total and particular areas of a geometric shape are calculated rather than total and particular outcomes.Filed Under: - Q:
## What are geometric patterns?

A:A geometric pattern is a pattern consisting of lines and geometric figures, such as triangles, circles and squares, that are arranged in a repeated fashion. Geometric patterns are found in many places, including art and architecture, and they tend to be symmetrical.

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## What is the explicit formula for the geometric sequence?

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Full Answer >**The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1).**The variable a_n is equal to the value of the nth term in the given geometric sequence, while a_1 is the value of the first term in the sequence.Filed Under: