geometric

(adjective)

increasing or decreasing in a geometric progression, i.e. multiplication by a constant.

Related Terms

Examples of geometric in the following topics:

  • Geometric Sequences

    • A geometric progression, also known as a geometric sequence, is an ordered list of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio $r$.
    • The $n$th term of a geometric sequence with initial value $a$ and common ratio $r$ is given by
    • The common ratio of a geometric series may be negative, resulting in an alternating sequence.
    • For instance: $1,-3,9,-27,81,-243, \cdots$ is a geometric sequence with common ratio $-3$.
    • The behavior of a geometric sequence depends on the value of the common ratio.

  • Introduction to geometric distribution (special topic)

    • These questions can be answered using the geometric distribution.
    • We first formalize each trial – such as a single coin flip or die toss – using the Bernoulli distribution, and then we combine these with our tools from probability (Chapter 2) to construct the geometric distribution.

  • Infinite Geometric Series

    • Geometric series are one of the simplest examples of infinite series with finite sums.
    • A geometric series is an infinite series whose terms are in a geometric progression, or whose successive terms have a common ratio.
    • If the terms of a geometric series approach zero, the sum of its terms will be finite.
    • A geometric series with a finite sum is said to converge.
    • Find the sum of the infinite geometric series $64+ 32 + 16 + 8 + \cdots$

  • Pottery in the Greek Geometric Period

    • The Geometric period in Greek art is distinguished by a reliance on geometric shapes to create human and animal figures as well as abstract décor.
    • In the Geometric period that followed, figures once more became present on the vessel.
    • Every empty space in these scenes is filled with geometric shapes—M's, diamonds, starbursts—demonstrating the Geometric painter's horror vacui.
    • Geometric Amphora, from the Dipylon Cemetery, Athens, Greece, c. 740 BCE.
    • Geometric Krater.

  • Geometric Symbolism

    • Throughout history, geometric designs have been ascribed with symbolic and sacred meaning.
    • Geometric designs have been used throughout history as religious and spiritual symbols.
    • Symbolic and sacred meanings are often ascribed to certain geometric shapes and geometric proportions.
    • Symmetry and other geometric patterns are often regarded as spiritually significant, symbolizing balance and order.Geometric ratios and figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture.
    • This sand mandala is an example of a sacred geometric design in Buddhist religious tradition.

  • Sculpture in the Greek Geometric Period

    • Ancient Greek sculpture of the Geometric period, although derived from geometric shapes, bears evidence of artistic observation of nature in some circumstances.
    • Ancient Greek sculpture of the Geometric period, although derived from geometric shapes, bears evidence of artistic observation of nature in some circumstances.
    • While the animals and people are based in basic geometric shapes, the artists clearly observed their subjects in order to highlight distinguishing characters.
    • Identify the key characteristics of the sculpture produced during the Geometric period.

  • Summing the First n Terms in a Geometric Sequence

    • By utilizing the common ratio and the first term of a geometric sequence, we can sum its terms.
    • The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant.
    • The following are several geometric series with different common ratios.
    • For $r\neq 1$, the sum of the first $n$ terms of a geometric series is:
    • Calculate the sum of the first $n$ terms in a geometric sequence

  • Notation for the Geometric: G = Geometric Probability Distribution Function X ~ G(p)

    • Read this as "X is a random variable with a geometric distribution. " The parameter is p. p = the probability of a success for each trial.
    • The geometric parameter list is (p, number) If "number" is left out, the result is the geometric probability table.

  • Log Transformations

    • The comparison of the means of log-transformed data is actually a comparison of geometric means.
    • This occurs because, as shown below, the anti-log of the arithmetic mean of log-transformed values is the geometric mean.Table 1 shows the logs (base 10) of the numbers 1, 10, and 100.
    • Therefore, if the arithmetic means of two sets of log-transformed data are equal then the geometric means are equal.

  • Applications of Geometric Series

    • Geometric series have applications in math and science and are one of the simplest examples of infinite series with finite sums.
    • Geometric series are used throughout mathematics.
    • The formula for the sum of a geometric series can be used to convert the decimal to a fraction:
    • In the case of the Koch snowflake, its area can be described with a geometric series.
    • Apply geometric sequences and series to different physical and mathematical topics