who found the rose classical curve?
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This curve was named rhodonea by the Italian mathematician Guido Grandi between 1723 and 1728 because it resembles a rose.\nI guess the name rose stuck later...
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The English Roses \nby Madonna, Jeffrey Fulvimari (Illustrator)
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Lagrange is considered the father of calculus.
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Two mathematicians, James Gregory (1638-1675) and Gottfried Wilhelm Leibniz (1646-1716), each working independantly of one another, discovered an infinite series for arctan x in the 1670's. This arctangent series led to the first ever found infinite series for .
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Go to http://en.wikipedia.org/wiki/Real_numbers#History.
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I think it was in "Bill and Ted's Bogus Journey".  Check it out here:\n\nhttp://en.wikipedia.org/wiki/Every_Rose_Has_Its_Thorn
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a) The curve you need is called a cycloid. Look that up on the web.\n\nb) The parametric form of the cycloid is\n\nx=12(a-sin a)      y=12(1-cos a) where a is then angular displacement. 24pi (circumference) will be the period and it passes through (0,0)
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Look up Gauss. Story is he added up 1..100 in grade school and invented the n*(N+1)/2.
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A graph of many rates (rate of reaction, population growth, etc.) produce exponential curves (asymptotic).\nThese are difficult to interpret.\nTo linearise the curve plot log y against x, or log y against log x. The properties of the rate can now easily be established.\nHave a look here (note, second reference is PDF format):
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Everything you wanted to know about a transformation curve. [please see link]
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Rene Descartes (the Cartesian coordinate plane plus many other contributions)\n\nPierre de Fermat\n\nBlaise Pascal\n\nLook them up. That can get you started. Personally, I'm going to bed.
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Differentiation of a function mapping R into R considers the limiting case of a secant to the curve to get the unique tangent line to the curve at each point. Ie., if we have a graph y=f(x), then the slope of a secant line between two points (x,f(x)) and (x+h, f(x+h)) on the curve is [f(x+h) - f(x)]/[x+h - x] = [f(x+h) - f(x)]/h. The tangent line to the curve at the point (x, f(x)) is hypothesized to have the slope given by the limit of the secant's slope as we rotate the secant so that the second intersection point moves closer to (x,f(x)). Algebraically, we want to study the limit of the above quotient as h approaches 0. The usefulness of the tangent at each point is that such a line gives a linear approximation to whatever f(x) stands for at each point. The tangent line also tells you when there is a maximum or minimum, as the line will be horizontal there (for certain well-behaved curves).\nThe first half of your study of calculus will involve justifying this concept and making concrete and mathematically precise what we mean when we say we are going to take the limit of an expression.\nThe second half of your calculus course will concetrate on integration, which studies the problem of calculating the area of arbitrarily shaped regions (instead of just the simple geometrical shapes you've studied before). Given an arbitrary curve y=f(x) or a bunch of curves enclosing a region, you will be able to calculate the area contained in the region. The motivation for the integral also involves limiting behavior. In the case of the Riemann integral, the hypothesis is that you can cover the area between a curve and the x-axis by a finite amount of rectangles, each with a finite area, and as the width of the rectangles get smaller, the difference between their total area and the true area under the curve goes to 0. The rigorous proof of this concept will be given by your textbook or teacher.\nYou will also study the Fundamental Theorem of Calculus, which connects the behavior of integrals to the behavior of derivatives in such a fundamental way that integrals are also known as antiderivatives. This theorem makes evaluating integrals a lot easier.\nAs you study further in higher-dimensional calculus and manifold theory, you will learn more general ways of thinking about derivatives and integrals, in that you will simply view them as forms over fields. We know all about linear algebra; we have to use derivatives to reduce the study of nonlinear forms to our familiar territory of linear algebra. This view is very useful in theoretical physics and differential geometry.\n\nAs some examples, let's study a curve we know well, the parabola y=x^2. To spice this up a little, let the parabola be the path of a bullet fired at some (horizontal) muzzle velocity v. Then from physics we know y(t) = -4.5*t^2 + 1 and horizontally x(t)=vt, so the path of the bullet is given by y(x) = (-4.5/v^2)x^2 + 1. We want to know how hard the bullet will hit the ground, so we need to know the instantaneous velocity of the bullet when y=0, which is when x=v/Sqrt[4.5] and thus t=Sqrt[4.5]. The velocity consists of the speed and direction of the bullet. First we get the direction, which is the slope of y(x) when y=0. Let -4.5/v^2 = k. Thus we want to study the quotient [f(x+h) - f(x)]/h = [ k(x+h)^2 + 1 - kx^2 - 1]/h = k*[x^2 + 2xh + h^2 - x^2]/h = k*[2xh + h^2]/h = k*[2x + h] as h approaches zero, which is just 2kx, so we have 2*(-4.5/v^2)*(v/Sqrt[4.5]) = -2*Sqrt[4.5]/v so the final slope decreases in absolute magnitude as muzzle velocity increases, as one would intuitively expect. The speed is a little more tedious, but if you've followed the above, you can do it yourself in no time.\nIntegration at this level requires knowledge of series and limits; if you're interested, pick up a good calculus text.
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intgral(from - infinity to infinity) of e^(-x^2)= sqrt(pi)\n\nThis is the area under the bell curve. It comes up very often in statistics.
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You take pie are squared and you sit on it and rotate.\n\nHold on, that's not right -- you subract it from the area of the square in which the circle fits snugly.  \nWhat's up with the 3' rise anyway?\n\nThe secret of the whole thing is "pie are squared", it's an ancient formuale that has worked well down through the years, in spite of the fact that it works out to millions of decimal places and then all the philosophical issues that come up -- and then when you talk about the Pothygorean theorem the plot really thickens.  Hold on, I've lost my train of thought.
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Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. Sometimes known as "the prince of mathematicians", Gauss had a remarkable influence in many fields of mathematics and science and is ranked beside Euler, Newton and Archimedes as one of history's greatest mathematicians.
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I don't think it was really invented by anyone.  Below is an article on the normal distribution, which the empirical rule is based on.  It gives a brief history of the normal distribution.
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I guess my favorite is sin(x). The graph of sin(x) is pure and simple. Starting at the origin like many other famous functions, it curves up to a maximum, curves down to a negative minimum, and returns to the x-axis. This graph is reflected everywhere in nature, from wheels, pendulums, and other physics-related concepts. Also, the area enclosed by one half of a sin(x) curve and the x-axis is 2. How cool is that! Sin(x) is better than all the other trignometric functions because it is the easiest to use.