![]() The method of exhaustion was described by the ancient Greek astronomer Eudoxus (ca. Even the ancient Greeks had developed a method to determine integrals via the method of exhaustion, which also is the first documented systematic technique capable of computing areas and volumes. For approximation, you don’t need modern integral calculus to solve this problem. To determine the area of curved objects or even the volume of a physical body with curved surfaces is a fundamental problem that has occupied generations of mathematicians since antiquity. – Wilhelm Gottfried Leibniz, Dissertatio Exoterica De Statu Praesenti et Incrementis Novissimis Deque Usu Geometriae (Spring 1676) The Area under the Curve “Only geometry can hand us the thread the labyrinth of the continuum’s composition, the maximum and the minimum, the infinitesimal and the infinite and no one will arrive at a truly solid metaphysic except he who has passed through this. His achievements are so numerous that we will definitely have more articles in the future about his contributions to science. But, Leibniz was kind of a universal polymath. We already dedicated an article at the SciHi blog to Leibniz and his works. Today, Gottfried Wilhelm Leibniz as well as independently Sir Isaac Newton are considered to be the founders of infinitesimal calculus. In general, infinitesimal calculus is the part of mathematics concerned with finding tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems. Integral calculus is part of infinitesimal calculus, which in addition also comprises differential calculus. On November 11, 1675, German mathematician and polymath Gottfried Wilhelm Leibniz demonstrates integral calculus for the first time to find the area under the graph of y = ƒ(x). Learner, Thinker, Writer: Jack Parrish teaches language arts and social studies in Fifth Grade.Gottfried Wilhelm Leibniz (1646 – 1716) Painting by Christoph Bernhard Francke To find that information, Newton ended up creating what we now know as integral and differential calculus. ![]() Taking a few months to think and ponder the problem, he came back with the solution that the orbits were parts of conic sections, thus the ellipse shape. When asked for an explanation of why the planets orbit in ellipses, Newton did not know. He mentions many of Newton’s famous discoveries, but his main evidence of why Newton was so great is the following. In the video, Tyson answers why he thinks Sir Isaac Newton is the greatest physicist. ![]() Neil deGrasse Tyson is a recognized American astrophysicist who is currently the director of the Hayden Planetarium in New York City. The picture has become associated with an “Internet Meme” (again, Google) and the person has become somewhat of a folk hero in the subculture of several Internet communities because of his forward, progressive thinking.ĭr. I came across the video below while looking for the source of the picture above. Nature, family, freestyle canoeing (Google it), and growth were all considered, but alas, I am too literal for that and I figured I would share what I really learned this afternoon. Surely inspiration would hit me a column of light shining from above would appear and I would be saved! Since that encounter this morning I’ve gone through a list of things that I could (should) write about. “You’re being authentic!” my coordinator said. This morning, I could not think of anything that I had learned. When I signed up for this post I began thinking of all the possible things to write about and felt inspired to share with the Trinity community my ability to connect phrases and words in lovely syntax and prose that they would, undoubtedly, praise. ![]()
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