what is archimedies principle?
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The archimedes principle is any object wholly or partly immersed in fluid will be buoyed up by a force equal to the weight of the fluid displaced by the object.
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There are LOTS. Pauli Exclusion Principle. Newton's Laws. Kepler's Laws. Galileo had some principles that might be called laws. Thermodynamic laws. Heisenberg Uncertainty Principle. Refraction Law. Ideal Gas Law. Boyle's Law. Charles Law. Biot-Savart Law. And so on and so forth. Hookie's law. \n\nStart researching.
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If you are referring to an area of a circle then Archimedes did that a while ago by method of exhoustion. http://people.bath.ac.uk/slt20/archimedesmethod.html \n\nHowever I think you are looking for a derivation in Cartesian coordinates.\n1.Determine what is the relationship of a radius to the x and y. \nFrom Pythagorean theorem x^2 + y^2 = r^2, where radius r is the hypotenuse. \n2.The equation above is good but not general enough since it does not incorporates shifts in x and y axis.  The x-a shifts to the right and x + a shifts the circle to the left. Similarly for y. then we have a general equation\n\n(x-a)^2 + (y-b)^2=r^2  \n\n\nI hope that helps.
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The formula is credited to Heron of Alexandria in the 1st century, and a proof can be found in his book Metrica. It is now believed that Archimedes already knew the formula, and it is of course possible that it has been known long before.\n\nLet the sides of a triangle have lengths a,b and c. Introduce the semiperimeter p = (a + b + c)/2 and the area S. Then Heron's formula asserts that\n S2 = p(p - a)(p - b)(p - c)\n\nW.Dunham analyzes the original Heron's proof in his Journey through Genius.\n\nFor the right triangle with hypotenuse c, we have S = ab/2. We'll modify the right hand side of the formula by noting that\n p - a = (- a + b + c)/2, p - b = (a - b + c)/2, p - c = (a + b - c)/2\n\nIt takes a little algebra to show that\n \n(a + b + c)(- a + b + c)(a - b + c)(a + b - c)\n= 2a2b2 + 2a2c2 + 2b2c2 - (a4 + b4 + c4)\n\nFor the right triangle, this expression is equal to 16S2 = 4a2b2. So we have\n 4a2b2= 2a2b2 + 2a2c2 + 2b2c2 - (a4 + b4 + c4)\n\nTaking all terms to the left side and grouping them yields\n (a4 + 2a2b2 + b4) - 2a2c2 - 2b2c2 + c4 = 0\n\nWith a little more effort\n (a2 + b2)2 - 2c2(a2 + b2) + c4 = 0\n\nAnd finally\n [(a2 + b2) - c2]2 = 0\nRemark\n\nFor a quadrilateral with sides a, b, c and d inscribed in a circle there exists a generalization of Heron's formula discovered by Brahmagupta. In this case, the semiperimeter is defined as p = (a + b + c + d)/2. Then the following formula holds\n S2 = (p - a)(p - b)(p - c)(p - d)\n\nSince any triangle is inscribable in a circle, we may let one side, say d, shrink to 0. This leads to Heron's formula.\n\nFor more information you can go to www.wikipedia.com  \nhttp://mathworld.wolfram.com/HeronsFormula.html\nhttp://www.cut-the-knot.org/pythagoras/herons.shtml\n\nI hope this helps! =-)
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If you're speaking of the motion of Earth on it's axis or it's rotation about the sun, the answer is the scientific principle of Inertia, read now!\n\nThe principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces.Inertia is the property of an object to resist changes in velocity unless acted upon by an outside force.Inertia is dependent upon the mass and shape of the object. The concept of inertia is today most commonly defined using Sir Isaac Newton's First Law of Motion, which states:\n\nEvery body perseveres in its state of being at rest or of moving uniformly straight ahead, except insofar as it is compelled to change its state by forces impressed. [Cohen & Whitman 1999 translation]\n\nThe description of inertia presented by Newton's law is still considered the standard for classical physics. However, it has also been refined and expanded over time to reflect developments in understanding of relativity and quantum physics which have led to somewhat different (and more mathematical) interpretations in some of those fields.\n\nNow read more at the links below:
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gas cools down if it expands suddenly.\n\nsimilar principle is used in AC and refrigerators.
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The Pythagorean Theorem? It's a^2 + b^2 = c^2.\n\nIf there's a right triangle, and a and b are the two "legs" (the shorter sides), and c is the hypotenuse (the longest side).
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Pythagoras Theorem asserts that for a right triangle with short sides of length a and b and long side of length c \na2 + b2 = c2 \n\nor c2-a2 = b2 \n\nhere is a link with all the necessary thing you have to know about this theorem . I hope it helps , just read it carefully and everything is going to be fine :)
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The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the same way about each vertex with all sides the same length (Cromwell 1997, pp. 91-92). \n\nThe Archimedean solids are distinguished by having very high symmetry, thus excluding solids belonging to a dihedral group of symmetries (e.g., the two infinite families of regular prisms and antiprisms), as well as the the elongated square gyrobicupola (because that surface's symmetry-breaking twist allows vertices "near the equator" and those "in the polar regions" to be distinguished; Cromwell 1997, p. 92). The Archimedean solids are sometimes also referred to as the semiregular polyhedra. \n\nThe Archimedean solids are illustrated below in alphabetical order (left to right, then continuing to the next row).
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It is a principle that can be either experimentaly shown or derived from quantum mechanical equations (shrodinger, dirac...) \nIt states that if you try to measure the value of a particles position and momentum you will always have an uncertanity of (&#92;hbar)/2 where &#92;hbar is basicly a h that is crossed like a "t".  It is planks constat divide by 2 (&#92;pi)\nso its around 10^(-34) Js\n\nthe principle it self says &#92;sigma_x &#92;sigma_p >= &#92;hbar /2\nwhere &#92;sigma_x is the standard deviation of x\n\nso if you take a bunch of identical systems and measure a particals possition and momentum you will not get exactly repeating results.  \n\n\nAlso notice that if you prepare the system such that the possition is exactly known the momentum can be any thing and vice versa.  \n\nBut that is the simple explination
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it's the Pythagorean Theorem\n\nIn any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
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Since ancient history regarding the concept.\n\nHistory of the notation:\n\nThe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιφέρεια (periphereia, the Greek word for periphery) or περίμετρον (perimetron), meaning 'measure around' in Greek.
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In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. They are related to the Copernican idea that the laws of physics should be the same everywhere in the universe, to the equivalence of gravitational and inertial mass, and also to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
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A device that was named the "Antikythera mechanism" bc discovered in 1900 in a sunken ship just off the coast of Antikythera, an island between Crete and the Greek mainland. It was dated to approximately 80 BC.\nGiven the age there is reason to believe that archimedes or his disciples might have been involved with developement of this device. But, at a minimum, the answer is the ancient greeks. It is as sophisticated as the babbage computer and was used to predict the positions of the sun moon and palnets on any date.
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think they are called axioms
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Every body that is in a fluid, or it is floating on the surface, or is sunk to the bottom loses an equal ammount of weight as the weight of the displaced fluid by the volume of the body.\n\nThe force that makes body's float or makes them lighter in a fluid (for ex. water) is called Archimed's force or Archimed's principle.\nIf this force is grater then the weight of the body (G=m*g) then the body floats on the surface.\n\nArchimed's force is greater if the density of the fluid is bigger. Oil has the density of 900 g/cm3 and water has the density of 1000 g/cm3. Because the reason why the objects are floating in oil and in water is of same nature, floating on oil is similar to floating on water.\nBut water has a bigger push force then oil.
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The only thing I know that is close is called the Johannes law\nand it is Astronomy\n\nI hope this is what you needed