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Decathlon Mathematics DR. MARY GARNER, PROFESSOR EMERITUS

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Decathlon Mathematics General mathematics, geometry and differential calculus Theme: New Alternatives in Energy: Ingenuity and Innovation Book: Anne Dillard’s Pilgrim at Tinker Creek

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Decathlon Mathematics “ I feel as though I stand at the foot of an infinitely high staircase, down which some exuberant spirit is flinging tennis ball after tennis ball, eternally, and the one thing I want in the world is a tennis ball.” ― Annie Dillard, Pilgrim at Tinker CreekAnnie DillardPilgrim at Tinker Creek “Push it. Examine all things intensely and relentlessly.” ― Annie Dillard, Pilgrim at Tinker CreekAnnie DillardPilgrim at Tinker Creek

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Decathlon Mathematics “She brings into her discussions knowledge from the whole spectrum of thought - referencing physics, literature, numerous religious traditions, anthropology, medicine and folklore -- just to name a few of her sources.” --http://sandra.stahlman.com/dillard.html

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This Presentation One Geometry problem One Calculus problem with an historical view, always considering infinity, and applied to solar energy

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Geometry/Calculus Archimedes – 3 rd century B.C. https://www.cs.drexel.edu/~crorres/Archimedes/contents.html Archimedes proved, among many other geometrical results, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder.

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Method of Exhaustion An equilateral triangle is inscribed in a circle with radius r. What is the area of each of the isosceles triangles shown? What is the area of the equilateral triangle?

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Method of Exhaustion

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An square is inscribed in a circle with radius r. What is the area of each of the triangles shown? What is the area of the square?

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Method of Exhaustion A regular pentagon is inscribed in a circle with radius r. What is the area of each of the triangles shown? What is the area of the pentagon?

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Method of Exhaustion A regular hexagon is inscribed in a circle with radius of r. What is the area of each of the triangles shown? What is the area of the hexagon?

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Method of Exhaustion What’s the pattern?

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More Archimedes Infinite Secrets … NOVA

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Geometry/Calculus and Solar Energy ability/Solar-Panels-Energy-and-Area- Under-Curve-Teacher-Guide.pdf sustainability/Solar-Panel-Lesson.pdf

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Geometry/Calculus and Solar Energy Energy is usually measured in kWh which stands for kilowatt hours. Energy = Power x Time Power is the rate at which energy is flowing through the system( 1 watt = 1 joule per sec). So the power associated with ten 100-watt bulbs all on at the same time is 10 x 100 = 1000 watts or 1 kW. The energy used by ten 100-watt bulbs, burned for 3 hours would be 3 kWh. Power is the derivative of energy and energy is the integral of power.

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Geometry/Calculus and Solar Energy https://enlighten.enphaseenergy.com/pv/public_systems/faZD132956

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Geometry/Calculus and Solar Energy How fast is power Increasing at t = 9 hours?

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Geometry/Calculus and Solar Energy

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What about Energy? Energy = Power x Time

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Geometry/Calculus and Solar Energy What about Energy? Energy = Power x Time = area under the curve

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Geometry/Calculus and Solar Energy What about Energy? Energy = Power x Time = area under the curve

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Geometry/Calculus and Solar Energy What about Energy? Energy = Power x Time = area under the curve

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Geometry/Calculus and Solar Energy https://enlighten.enphaseenergy.com/pv/public_systems/faZD132956

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Geometry/Calculus and Solar Energy

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Decathlon Mathematics “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of reality? —Albert Einstein The "great book" of the universe is written in the language of mathematics, he (Galileo) famously declared, and unless we understand the triangles, circles, and other geometrical figures that form its characters, he wrote, "it is humanly impossible to comprehend a single word of it [and] one wanders in vain through a dark labyrinth.“ -- "Just as music is auditory patterns that the human mind finds pleasant, mathematics captures patterns that the universe finds pleasant, if you like— patterns that are implicit in the way the universe works.“ – Keith Devlin

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Thank you! Mary Garner “Push it. Examine all things intensely and relentlessly.” ― Annie Dillard, Pilgrim at Tinker CreekAnnie DillardPilgrim at Tinker Creek And what will you find?

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Thank you! Mary Garner “Push it. Examine all things intensely and relentlessly.” ― Annie Dillard, Pilgrim at Tinker CreekAnnie DillardPilgrim at Tinker Creek And what will you find? Mathematics!

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