Area | History of calculus | Geometry | Volume | Mathematical principles
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: * 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas. * 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes. Today Cavalieri's principle is seen as an early step towards integral calculus, and while it is used in some forms, such as its generalization in Fubini's theorem, results using Cavalieri's principle can often be shown more directly via integration. In the other direction, Cavalieri's principle grew out of the ancient Greek method of exhaustion, which used limits but did not use infinitesimals. (Wikipedia).
The golden ratio | Lecture 3 | Fibonacci Numbers and the Golden Ratio
The classical definition of the golden ratio. Two positive numbers are said to be in the golden ratio if the ratio between the larger number and the smaller number is the same as the ratio between their sum and the larger number. Phi=(1+sqrt(5))/2 approx 1.618. Join me on Coursera: http
From playlist Fibonacci Numbers and the Golden Ratio
Cavalieri's principle - An example (Measure Theory Part 18)
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From playlist Measure Theory
6 AWESOME DEMOS of Bernoulli's law!
In this video i show some simple experiments about Bernoulli' s law "coanda effect" and how airplane fly. Enjoy!
From playlist MECHANICS
Product measure and Cavalieri's principle (Measure Theory Part 17)
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From playlist Measure Theory
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Prinzip von Cavalieri - Beispiel
English version here: https://youtu.be/cpQRRLNA5GA Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Offizielle Unterstützer in diesem Monat: - William Ripley - Petar Djurkovic - Mayra Sharif - Dov Bulka - Lukas Mührke - Khan El - Marco Molina
From playlist Maßtheorie und Integrationstheorie
Cavalieri's Principle Calculus - Vertical Cross Sections
0:00 - 1:00 - Intro - Explanation of concept of Cavalieri's Principle 1:00 - 6:55 - Question 1 (No Calculator) 6:55 - 14:55 - Question 2 (Calculator) 14:55 - 18:19 - Question 3 (No calculator) In this video I go through 3 examples showing how to use Cavalieri's Principle with integration
From playlist Calculus 1
Produktmaß und Prinzip von Cavalieri
English version here: https://youtu.be/BTU69ezkpZw Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Offizielle Unterstützer in diesem Monat: - William Ripley - Petar Djurkovic - Mayra Sharif - Dov Bulka - Lukas Mührke Hier erzähle ich etwas
From playlist Maßtheorie und Integrationstheorie
From playlist Level 2 NCEA Physics
AP Calculus AB 2019 Free Response question 5
In this video, I go through the AP Calculus AB 2019 Free Response question 5. The topics covered in this video include finding area between two curves, Cavalieri's Principle, volume of solids of revolution about a line. As I go through the solutions, I talk about the rubrics used to evalua
From playlist AP Calculus AB/BC Review
Friedrich Nietzsche had a particular fondness for a concept called (in Latin) 'amor fati', a Stoic acceptance of one's fate and a commitment to embrace reality, in all its beauty and pain. For gifts and more from The School of Life, visit our online shop: https://goo.gl/dNX5UF Join our mai
From playlist WESTERN PHILOSOPHY
Without integration, why is the volume of a paraboloid half of its inscribing cylinder? (DIw/oI #8)
Rather than using integration, can we find the volume of a paraboloid? Yes, if we accept a precursor to calculus - Cavalieri's principle. Usually, integration is needed to find the volume of a paraboloid, for example using shell method, but using Cavalieri's principle, and a sneaky little
From playlist Novel topics (not in usual math curricula)
#Physics #Mechanics #Engineering #NicholasGKK #Shorts
From playlist General Mechanics
Fibonacci numbers and the golden ratio | Lecture 4 | Fibonacci Numbers and the Golden Ratio
Relationship between the Fibonacci numbers and the golden ratio. The ratio of consecutive Fibonacci numbers approaches the golden ratio. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: h
From playlist Fibonacci Numbers and the Golden Ratio
Indefinite integrals? Cavalieri’s quadrature? Complex analysis? | DIw/oI #6
In this last video of this video series, we are going to investigate a bunch of ideas that fall within the umbrella of "Doing integrals without integration", including indefinite integrals, an elementary way to derive Cavalieri's quadrature formula, as well as complex analysis as a tool.
From playlist Novel topics (not in usual math curricula)
Umberto Bottazzini, The immense sea of the infinite - 10 aprile 2019
https://www.sns.it/it/evento/the-immense-sea-of-the-infinite Umberto Bottazzini (Università degli Studi di Milano) The immense sea of the infinite Abstract In a celebrated talk Hilbert stated that the infinite was nowhere to be found in the real, external world. Yet from time immemorial
From playlist Colloqui della Classe di Scienze
Unique way to divide a tetrahedron in half
This is an interesting geometry volume problem using tetrahedrons. We use the volume of a tetrahedron and Cavalieri's principle in 3D.
From playlist Platonic Solids
The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).
From playlist Physics