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In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
A building's surface detailing, inside and outside, often includes decorative moulding, and these often contain ogee-shaped profiles—consisting (from low to high) of a concave arc flowing into a convex arc, with vertical ends; if the lower curve is convex and higher one concave, this is known as a Roman ogee, although frequently the terms are used interchangeably and for a variety of other ...
The figure-eight knot has genus 1 and is fibered. Therefore its complement fibers over the circle, the fibers being Seifert surfaces which are 2-dimensional tori with one boundary component. The monodromy map is then a homeomorphism of the 2-torus, which can be represented in this case by the matrix ( 2 1 1 1 ) {\displaystyle ({\begin ...
The title of the book has been translated in a wide variety of ways. In 1852, Alexander Wylie referred to it as Arithmetical Rules of the Nine Sections. With only a slight variation, the Japanese historian of mathematics Yoshio Mikami shortened the title to Arithmetic in Nine Sections.
In the Renaissance, an architect like Leon Battista Alberti was expected to be knowledgeable in many disciplines, including arithmetic and geometry.. The architects Michael Ostwald and Kim Williams, considering the relationships between architecture and mathematics, note that the fields as commonly understood might seem to be only weakly connected, since architecture is a profession concerned ...
Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). [20]
A staircase or stairway is one or more flights of stairs leading from one floor to another, and includes landings, newel posts, handrails, balustrades, and additional parts. [5] In buildings, stairs is a term applied to a complete flight of steps between two floors. A stair flight is a run of stairs or steps
The word "algebra" is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing.