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  2. List of hyperboloid structures - Wikipedia

    en.wikipedia.org/wiki/List_of_hyperboloid_structures

    This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built his first example as a water tower ( hyperbolic shell ) for the 1896 All-Russian Exposition .

  3. Hyperboloid structure - Wikipedia

    en.wikipedia.org/wiki/Hyperboloid_structure

    Hyperboloid structures are superior in stability against outside forces compared with "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency). Hence they are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features.

  4. Category:Hyperboloid structures - Wikipedia

    en.wikipedia.org/.../Category:Hyperboloid_structures

    Pages in category "Hyperboloid structures" The following 35 pages are in this category, out of 35 total. This list may not reflect recent changes. ...

  5. Hyperboloid - Wikipedia

    en.wikipedia.org/wiki/Hyperboloid

    One-sheeted hyperboloids are used in construction, with the structures called hyperboloid structures. A hyperboloid is a doubly ruled surface; thus, it can be built with straight steel beams, producing a strong structure at a lower cost than other methods. Examples include cooling towers, especially of power stations, and many other structures ...

  6. Music and mathematics - Wikipedia

    en.wikipedia.org/wiki/Music_and_mathematics

    The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. While music theory has no axiomatic foundation in modern mathematics, the basis of musical sound can be described mathematically (using acoustics) and exhibits "a remarkable array of ...

  7. Hyperbolic group - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_group

    In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.

  8. List of set classes - Wikipedia

    en.wikipedia.org/wiki/List_of_set_classes

    This is a list of set classes, by Forte number. [1] In music theory, a set class (an abbreviation of pitch-class-set class) is an ascending collection of pitch classes, transposed to begin at zero. For a list of ordered collections, see this list of tone rows and series. Sets are listed with links to their complements.

  9. Musical form - Wikipedia

    en.wikipedia.org/wiki/Musical_form

    In music, form refers to the structure of a musical composition or performance.In his book, Worlds of Music, Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a piece of music, such as "the arrangement of musical units of rhythm, melody, and/or harmony that show repetition or variation, the arrangement of the instruments (as in the order of ...