In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, the special type of ellipse in which the two focal points are the same; the elongation of an ellipse is measured by its eccentricity e, a number ranging from e = 0 to e = 1. Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: x 2 a 2 + y 2 b 2 = 1. Assuming a ≥ b, the foci are for c = a 2 − b 2; the standard parametric equation is: = for 0 ≤ t ≤ 2 π. Ellipses are the closed type of conic section: a plane curve tracing the intersection of a cone with a plane. Ellipses have many similarities with the other two forms of conic sections and hyperbolas, both of which are open and unbounded. An angled cross section of a cylinder is an ellipse. An ellipse may be defined in terms of one focal point and a line outside the ellipse called the directrix: for all points on the ellipse, the ratio between the distance to the focus and the distance to the directrix is a constant.
This constant ratio is the above-mentioned eccentricity: e = c a = 1 − b 2 a 2. Ellipses are common in physics and engineering. For example, the orbit of each planet in the solar system is an ellipse with the Sun at one focus point; the same is true for all other systems of two astronomical bodies. The shapes of planets and stars are well described by ellipsoids. A circle viewed from a side angle looks like an ellipse: that is, the ellipse is the image of a circle under parallel or perspective projection; the ellipse is the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency: a similar effect leads to elliptical polarization of light in optics. The name, ἔλλειψις, was given by Apollonius of Perga in his Conics. An ellipse can be defined geometrically as a set or locus of points in the Euclidean plane: Given two fixed points F 1, F 2 called the foci and a distance 2 a, greater than the distance between the foci, the ellipse is the set of points P such that the sum of the distances | P F 1 |, | P F 2 | is equal to 2 a: E =.
The midpoint C of the line segment joining the foci is called the center of the ellipse. The line through the foci is called the major axis, the line perpendicular to it through the center is the minor axis; the major axis intersects the ellipse at the vertex points V 1, V 2, which have distance a to the center. The distance c of the foci to the center is called linear eccentricity; the quotient e = c a is the eccentricity. The case is included as a special type of ellipse; the equation | P F 2 | + | P F 1 | = 2 a can be viewed in a different way: If c 2 is the circle with midpoint F 2 and radius 2 a the distance of a point P to the circle c 2 equals the distance to the focus F 1: | P F 1 | = | P c 2 |. C
Colour Coding was an Australian indie pop band formed in 2011 and based in Sydney. The band was formed by both members of the group Operator Please; the band released its first EP Proof in March 2012 with the lead single "Perfect" uploaded as a free track online in November 2011. At ages 12 and 13, cousins Chris and Tim recorded an extended play in Tim's father's mark studio. In 2005, Tim joined the pop group Operator Please with several of his Gold Coast schoolmates, including founder and lead vocalist Amandah Wilkinson. In 2008, Chris joined the band as keyboardist; this early experience helped the boys realize their dream of forming Colour Coding. In September 2011, Hoppy Studios produced their first single, "Perfect", it was a free-to-download online release track. The track was added to the fourth digital release by New York label Cosine Records in the US. In March 2012, the duo released their debut extended play recorded at Sydney's Hurley Studios, titled Proof and introduced their first concerts.
On 30 November 2013, the duo announced on their official Facebook page that they would be entering a hiatus. EPsProof Proof Remixed Singles"Perfect" "Hold Tight" "Yours, Not Mine"/"Hanging On" Colour Coding's channel on YouTube Official page on Facebook Official account on Twitter Profile on Bandcamp
The Philosophic Thought of Ayn Rand is a 1984 collection of essays on Ayn Rand's philosophy of Objectivism, edited by Douglas Den Uyl and Douglas B. Rasmussen, it includes essays by nine different authors covering Rand's views in various areas of philosophy. The work received positive reviews, crediting it with bringing serious attention by philosophers to Rand and her work. However, reviewers noted that the work assumed considerable prior knowledge of philosophy on the part of the reader; the book is divided into three sections that represent different areas of philosophy addressed in Rand's thought. Each section starts with an essay by Den Uyl and Rasmussen, followed by essays from other contributors; the first section covers epistemology. It includes essays by Robert Hollinger; the second section covers ethics and contains essays by Jack Wheeler, Charles King, Erick Mack. The final section has essays by Antony Flew and Tibor R. Machan. Den Uyl and Rassmussen began work on the book; when she heard about the project, she discouraged it, as she had done with other projects.
Rand died in 1982, work on the book proceeded despite her disapproval. The Philosophic Thought of Ayn Rand was first published by as a hardcover book by the University of Illinois Press in 1984, they released it as a paperback in 1986. Sidney Gendin gave The Philosophic Thought of Ayn Rand a positive review in Library Journal, writing that the work redressed the neglect of Rand's work by academic philosophers, avoided being uncritical of Rand, revealed interesting parallels between Rand and writers such as Gilbert Ryle and J. L. Austin. However, he noted that the book assumed that the reader had "considerable background in general philosophy". A review in The Freeman praised the book as "a valuable beginning by serious philosophers at the important task of evaluating and developing Rand's philosophy, in a dispassionate, objective manner."In Reason, Randall Dipert wrote that the book "marks a turning point" in getting professional philosophers engaged with Rand's ideas, but was not "uniformly successful".
Rand scholar Mimi Reisel Gladstein described it as "a major contribution to Rand scholarship", although not always approachable for readers not versed in academic philosophy. In 2003, Chris Matthew Sciabarra identified The Philosophic Thought of Ayn Rand as one of several books that reflected a growing interest in Rand after her death. "The Randian Argument Reconsidered: A Reply to Charles King", a paper by Paul St. F. Blair responding to King's essay in this volume