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Frustum Meaning: Definition, Examples, and Translations

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frustum

[หˆfrสŒstษ™m ]

Definition

Context #1 | Noun

geometry shape

A frustum is the portion of a solid (normally a cone or a pyramid) that lies between two parallel planes cutting it. It can be described as a shape that has a smaller base and a larger base, joined by a curved or flat surface. The frustum is commonly used in geometry, architecture, and engineering. The volume and surface area of a frustum can be calculated using specific formulas.

Synonyms

truncated cone, truncated pyramid.

Examples of usage

  • The frustum of a cone is often used in engineering designs.
  • To calculate the volume of a frustum, you need both the radii of the bases.
  • The frustum shape was utilized in the design of the new skyscraper.
  • The cake was shaped like a frustum, wider at the bottom and narrower at the top.

Translations

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Interesting Facts

Mathematics

  • Frustums are often studied in geometry to understand properties of solids and calculate volumes and surface areas.
  • The volume of a frustum can be calculated using a specific formula that involves the radii of the two bases and the height.
  • Frustums can be seen in everyday objects like cups, lampshades, and even traffic cones, helping to connect geometry to real life.

Architecture

  • The frustum shape is commonly used in architecture, especially in structures like columns and domes, to provide stability and aesthetic appeal.
  • Famous architectural elements, such as the frustum-shaped pyramids in ancient civilizations, served both practical and symbolic purposes.
  • In modern design, frustums are utilized to create dynamic, visually interesting forms in buildings and interiors.

Science

  • In physics, frustums are relevant when analyzing the properties of various materials and their weight distribution.
  • The concept of frustums is important in engineering, particularly in the design of components like funnels and pipes, ensuring efficient flow.
  • They also appear in fields like astronomy, where telescope mirrors might be designed in frustum shapes for better light collection.

Art and Design

  • Artists and designers exploit the frustum shape to create visually engaging sculptures and installations that play with perspective.
  • In visual art, understanding shapes like frustums aids in creating three-dimensional effects, enhancing the realism of their work.
  • Frustums often inspire creativity in product design by combining functionality with aesthetic shapes.

Origin of 'frustum'

Main points about word origin

  • The word 'frustum' comes from Latin, meaning 'a piece' or 'a slice' โ€“ referring to the shape being a section of a larger object.
  • In geometry, this term has been used since at least the 17th century, highlighting its long-standing presence in mathematical discussions.
  • Itโ€™s commonly used in the context of cones and pyramids, where the top portion is removed.

The term 'frustum' originates from Latin, derived from the word 'frustum' meaning 'a piece cut off'. The concept of frustum has been traced back to ancient Greek and Roman geometric studies, where mathematicians studied solids and their properties. The use of frustums in architecture and engineering has increased over the centuries, allowing for innovative designs in various fields. The understanding of frustums has evolved through the work of mathematicians throughout history, enhancing both theoretical and practical applications in modern geometry.

Word Frequency Rank

This word's position of #33,060 indicates it's among the more rare English words. While understanding it broadens your vocabulary, focus on more common words first.