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Following Archimedes' argument in The Measurement of a Circle (c. 260 BCE), compare the area enclosed by a circle to a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius. If the area of the circle is not equal to that of the triangle, then it must be either greater or less.
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π. [a] Thus the circumference C is related to the radius r and diameter d by: = =.
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Gaius Julius Caesar [a] (12 July 100 BC – 15 March 44 BC) was a Roman general and statesman. A member of the First Triumvirate, Caesar led the Roman armies in the Gallic Wars before defeating his political rival Pompey in a civil war, and subsequently became dictator from 49 BC until his assassination in 44 BC.
Thus, when the radius is small enough, these sets degenerate to the equilateral triangle itself, but when the radius is as large as possible they equal the corresponding Reuleaux triangle. Every shape with width w, diameter d, and inradius r (the radius of the largest possible circle contained in the shape) obeys the inequality
Augustus Caesar is at the top of the scale. He was also added in the expansion Civilization IV: Warlords as a Roman leader, accompanying Julius Caesar from the original game. Augustus also makes his way into Civilization V, once again leading the Roman Empire. His special ability is "The Glory of Rome", which grants production bonuses for city ...
The term "First Triumvirate", while well-known, is a misleading one which is regularly avoided by modern scholars of the late republic. Boards of a certain number of men such as decemviri were a feature of Roman administration, but this alliance was not one of them.