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Mamikon Mnatsakanian
MAMIKON A. MNATSAKANIAN (Armenian : Մամիկոն Մնացականյան) is Project Associate at Project Mathematics! at the California Institute of Technology
California Institute of Technology
. He received a Ph.D. in physics in 1969 from Yerevan State University , where he became professor of astrophysics. As an undergraduate he specialized in the development of geometric methods for solving calculus problems by a visual approach that makes no use of formulas, which he later developed into his system of visual calculus . In 2010 he was nominated by Caltech for the Ambartsumians International Prize , awarded annually by the President of Armenia , for his contributions in the field of theoretical astrophysics . In 1959 he discovered a new proof of the Pythagorean theorem
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Theoretical Astrophysics
ASTROPHYSICS is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the heavenly bodies , rather than their positions or motions in space." Among the objects studied are the Sun , other stars , galaxies , extrasolar planets , the interstellar medium and the cosmic microwave background . Their emissions are examined across all parts of the electromagnetic spectrum , and the properties examined include luminosity , density , temperature , and chemical composition. Because astrophysics is a very broad subject, astrophysicists typically apply many disciplines of physics, including mechanics , electromagnetism , statistical mechanics , thermodynamics , quantum mechanics , relativity , nuclear and particle physics , and atomic and molecular physics . In practice, modern astronomical research often involves a substantial amount of work in the realms of theoretical and observational physics
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Pythagorean Theorem
In mathematics , the PYTHAGOREAN THEOREM, also known as PYTHAGORAS\'S THEOREM, is a fundamental relation in Euclidean geometry among the three sides of a right triangle . It states that the square of the hypotenuse (the side opposite the right angle ) is equal to the sum of the squares of the other two sides . The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation": a 2 + b 2 = c 2 , {displaystyle a^{2}+b^{2}=c^{2},} where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras
Pythagoras
(c. 570–495 BC) as it is he who, by tradition, is credited with its first recorded proof
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Wolfram Demonstrations Project
The WOLFRAM DEMONSTRATIONS PROJECT is an organized, open-source collection of small interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hosted by Wolfram Research , whose stated goal is to bring computational exploration to the widest possible audience. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents\' Choice Award in 2008. CONTENTS * 1 Technology * 2 Topics * 3 Process * 4 Alternatives * 5 References * 6 External links TECHNOLOGYThe Demonstrations run in Mathematica 6 or above and in Wolfram CDF Player which is a free modified version of Wolfram's Mathematica and available for Windows, Linux and Macintosh and can operate as a web browser plugin
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Special
SPECIAL or SPECIALS may refer to: CONTENTS * 1 Music * 2 Film and television * 3 Other uses * 4 See also MUSIC * Special (album) , a 1992 album by Vesta Williams * "Special" (Garbage song) , 1998 * "Special" (Mew song) , 2005 * "Special" (Stephen Lynch song) , 2000 * The Specials
The Specials
, a British band * "Special", a song by Violent Femmes on The Blind Leading the Naked * "Special", a song on
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Armenian Language
The ARMENIAN LANGUAGE (classical : հայերէն; reformed : հայերեն hayeren) occupies an independent branch of the Indo-European language tree. It is the official language of the Republic of Armenia
Armenia
and the Republic of Artsakh
Republic of Artsakh
. It has historically been spoken throughout the Armenian Highlands
Armenian Highlands
and today is widely spoken in the Armenian diaspora . Armenian is written using the Armenian alphabet
Armenian alphabet
, introduced in AD 405 by Mesrop Mashtots . Armenian has developed since the separation from Indo-European mother tongue in the third millennium BC to at least the time of the first Armenian dynasty (the Yervanduni dynasty , founded in the 6th century BC). Hellenistic influences during the Artashesian Dynasty (2nd century BC to 1st century AD) led to word borrowings from Greek and Latin
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President Of Armenia
The PRESIDENT OF THE REPUBLIC OF ARMENIA (Armenian : Հայաստանի Հանրապետության Նախագահ, Hayastani Hanrapetutyan Nakhagah) is the head of state , supreme commander-in-chief and the guarantor of independence and territorial integrity of Armenia
Armenia

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Project Mathematics!
PROJECT MATHEMATICS! (stylized as PROJECT MATHEMATICS!), is a series of educational video modules and accompanying workbooks for teachers, developed at the California Institute of Technology to help teach basic principles of mathematics to high school students. In 2017, the entire series of videos was made available on YouTube
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Yerevan State University
YEREVAN STATE UNIVERSITY (YSU; Armenian : Երևանի Պետական Համալսարան, ԵՊՀ, Yerevani Petakan Hamalsaran) is the oldest continuously operating public university in Armenia
Armenia
. Founded in 1919, it is the largest and most prestigious university in the country. It is thus informally known as Armenia's "mother university" (Մայր ԲՈւՀ, Mayr Buh). Of its 3,150 employees, 1,190 comprise the teaching staff which includes 25 academicians, 130 professors, 700 docents (associate professors), and 360 assistant lecturers. The university has 400 researchers, 1,350 post-graduate students, and 8,500 undergraduates, including 300 students from abroad. Instruction is in Armenian , but instruction in Russian and English for foreign students is arranged according to need. The academic year is from September 1 through June 30
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California Institute Of Technology
The CALIFORNIA INSTITUTE OF TECHNOLOGY (abbreviated CALTECH ) is a private doctorate-granting university located in Pasadena, California , United States. Although founded as a preparatory and vocational school by Amos G. Throop in 1891, the college attracted influential scientists such as George Ellery Hale
George Ellery Hale
, Arthur Amos Noyes , and Robert Andrews Millikan in the early 20th century. The vocational and preparatory schools were disbanded and spun off in 1910, and the college assumed its present name in 1921. In 1934, Caltech was elected to the Association of American Universities , and the antecedents of NASA
NASA
's Jet Propulsion Laboratory
Jet Propulsion Laboratory
, which Caltech continues to manage and operate, were established between 1936 and 1943 under Theodore von Kármán
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Generalized Conic
In mathematics , a GENERALIZED CONIC is a geometrical object defined by a property which is a generalization of some defining property of the classical conic . For example, in elementary geometry , an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed points – the foci – in the plane is a constant. The curve obtained when the set of two fixed points is replaced by an arbitrary, but fixed, finite set of points in the plane is called an n–ellipse and can be thought of as a generalized ellipse. Since an ellipse is the equidistant set of two circles, the equidistant set of two arbitrary sets of points in a plane can be viewed as a generalized conic. In rectangular Cartesian coordinates , the equation y = x2 represents a parabola . The generalized equation y = x r, for r ≠ 0 and r ≠ 1, can be treated as defining a generalized parabola
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Visual Calculus
VISUAL CALCULUS by Mamikon Mnatsakanian (known as Mamikon) is an approach to solving a variety of integral calculus problems. Many problems that would otherwise seem quite difficult yield to the method with hardly a line of calculation, often reminiscent of what Martin Gardner calls "aha! solutions" or Roger Nelsen a proof without words . CONTENTS * 1 Description * 2 Applications * 2.1 Area of a cycloid * 3 See also * 4 References * 5 External links DESCRIPTION Illustration of Mamikon's method showing that the areas of two annuli with the same chord length are the same regardless of inner and outer radii. Mamikon devised his method in 1959 while an undergraduate, first applying it to a well-known geometry problem: Find the area of a ring (annulus ), given the length of a chord tangent to the inner circumference
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Mamikon Mnatsakanian
MAMIKON A. MNATSAKANIAN (Armenian : Մամիկոն Մնացականյան) is Project Associate at Project Mathematics! at the California Institute of Technology
California Institute of Technology
. He received a Ph.D. in physics in 1969 from Yerevan State University , where he became professor of astrophysics. As an undergraduate he specialized in the development of geometric methods for solving calculus problems by a visual approach that makes no use of formulas, which he later developed into his system of visual calculus . In 2010 he was nominated by Caltech for the Ambartsumians International Prize , awarded annually by the President of Armenia , for his contributions in the field of theoretical astrophysics . In 1959 he discovered a new proof of the Pythagorean theorem
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