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Great Comet Of 1264
The Great Comet of 1264 (C/1264 N1) was one of the brightest comets on record. It appeared in July 1264 and remained visible to the end of September. It was first seen during the evenings after sunset, but appeared in its greatest splendor in weeks afterward, when it became visible during the mornings in the northeastern sky, with the tail perceived long before the comet itself rose above the horizon. The head of the comet seemed like an obscure and ill-defined star, and the tail passed from this portion of it like expanded flames, stretching forth towards the mid-heavens to a distance of one hundred degrees from the nucleus. The comet of 1264 was described to have been an object of great size and brilliancy. The comet's splendor was greatest at the end of August and the beginning of September. At that time, when the head was just visible above the eastern horizon in the morning sky, the tail stretched out past the mid-heaven towards the west, or was nearly 100° in length. The chr ...
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Great Comet Of 1264
The Great Comet of 1264 (C/1264 N1) was one of the brightest comets on record. It appeared in July 1264 and remained visible to the end of September. It was first seen during the evenings after sunset, but appeared in its greatest splendor in weeks afterward, when it became visible during the mornings in the northeastern sky, with the tail perceived long before the comet itself rose above the horizon. The head of the comet seemed like an obscure and ill-defined star, and the tail passed from this portion of it like expanded flames, stretching forth towards the mid-heavens to a distance of one hundred degrees from the nucleus. The comet of 1264 was described to have been an object of great size and brilliancy. The comet's splendor was greatest at the end of August and the beginning of September. At that time, when the head was just visible above the eastern horizon in the morning sky, the tail stretched out past the mid-heaven towards the west, or was nearly 100° in length. The chr ...
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Ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity (mathematics), eccentricity e, a number ranging from e = 0 (the Limiting case (mathematics), limiting case of a circle) to e = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic solution for its area, but only approximations for its perimeter (also known as circumference), for which integration is required to obtain an exact solution. Analytic geometry, Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: : \frac+\frac = 1 . Assuming a \ge b, the foci are (\pm c, 0) for c = \sqrt. The standard parametric e ...
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13th Century In Science
In music or music theory, a thirteenth is the note thirteen scale degrees from the root of a chord and also the interval between the root and the thirteenth. The interval can be also described as a compound sixth, spanning an octave plus a sixth. The thirteenth is most commonly major or minor . A thirteenth chord is the stacking of six (major or minor) thirds, the last being above the 11th of an eleventh chord. Thus a thirteenth chord is a tertian (built from thirds) chord containing the interval of a thirteenth, and is an extended chord if it includes the ninth and/or the eleventh. "The jazzy thirteenth is a very versatile chord and is used in many genres." Since 13th chords tend to become unclear or confused with other chords when inverted, they are generally found in root position.Benward & Saker (2009). ''Music in Theory and Practice: Volume II'', p.179. Eighth Edition. . For example, depending on voicing, a major triad with an added major sixth is usually cal ...
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1264
Year 1264 ( MCCLXIV) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Spring – Battle of Makryplagi: Constantine Palaiologos, half-brother of Emperor Michael III (Palaiologos), resumes operations against the Principality of Achaea. He advances up in northern Elis, and sets up his camp at a location called "St. Nicholas of Mesiskli". Prince William II of Villehardouin with his own troops march to meet him and arrays his men ready for battle. The Byzantine vanguard under Michael Kantakouzenos, ride forth from the Byzantine lines, but the force is ambushed and Michael is killed by the Achaeans. Constantine retreats and goes on to lay siege to the fortress of Nikli. There, Turkish mercenaries (some 1,000 horsemen), confront him and demand that he pay them their arrears of 6 months. Constantine refuses, whereupon the Turkish troops desert to William. He decides to raise the siege and d ...
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Non-periodic Comets
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic. Definition A function is said to be periodic if, for some nonzero constant , it is the case that :f(x+P) = f(x) for all values of in the domain. A nonzero constant for which this is the case is called a period of the function. If there exists a least positive constant with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period. A function with period will repeat on intervals of length , and these intervals are sometimes also referred to as periods of the function. Geometrically, a ...
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Conic Section
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of