Works by Archimedes | Archimedes
Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is that of a certain inscribed triangle. It is one of the best-known works of Archimedes, in particular for its ingenious use of the method of exhaustion and in the second part of a geometric series. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He then computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of a reductio ad absurdum argument in ancient Greek mathematics, and Archimedes' solution remained unsurpassed until the development of integral calculus in the 17th century, being succeeded by Cavalieri's quadrature formula. (Wikipedia).
How to determine the domain and range and graph
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Episode 7: Integration - The Mechanical Universe
Episode 7. Integration: Newton and Leibniz arrive at the conclusion that differentiation and integration are inverse processes. “The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university physics course. E
From playlist The Mechanical Universe
What is the domain and range of a quadratic graph
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
How to compute area of curved shapes in 250 BC | Archimedes 'The Method' | #SoME2
This is my first video on an interesting topic from ancient mathematics and geometry that I came across, 'The method' of Archimedes to find area of a parabolic segment. 0:00 Introduction to Archimedes 2:05 Value of Pi 3:10 Area of Parabola 4:40 The Method 9:41 Conclude 10:58 The End [1]
From playlist Summer of Math Exposition 2 videos
Ancient Greeks (Archimedes) almost discovered calculus! | DIw/oI #4
Newton or Leibniz? This never-ending debate on who discovered calculus would be settled if ancient Greeks were not so afraid of the concept of infinitesimals. Archimedes' work calculates the area (called quadrature back then) enclosed by a parabola and a line (i.e. parabolic segment), whic
From playlist Geometry Gem
What is Calculus - Lesson 4 | Integration | Don't Memorise
In this video, we will understand the idea of integration. The basic idea of integration was known to people since ancient times, and it was called the method of exhaustion. But this method was not a general one that could be used for everything. The technique of integration is a general m
From playlist Calculus - Basics
Find the vertex of a polynomial
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Using the vertex determine the domain and range of a parabola
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Use the formula to find the vertex
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Mod-01 Lec-10 Numerical Integration: Basic Rules
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Determine the vertex and domain and range of a function
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Determine if a quadratic has a max or min value then find it (mistake)
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
How to develop a proper theory of infinitesimals I | Famous Math Problems 22a | N J Wildberger
Infinitesimals have been contentious ingredients in quadrature and calculus for thousands of years. Our definition of the term starts with the Wikipedia entry, modified a bit to reduce the dependence on "real numbers", which is actually quite unnecessary--- but as a logical definition it i
From playlist Famous Math Problems
How to determine the axis of symmetry and vertex
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Determine if a quadratic has a max or min as it's vertex
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola
Mod-01 Lec-13 Gauss 2-point Rule: Error
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
The integral of x^n (a) | Famous Math Problems 10 | NJ Wildberger
The integral of x^n is one of the two most important formulas in calculus. The cases n=0,1 and 2 go back to antiquity, and to Archimedes quadrature of a parabola. The general case was first enunciated by Cavalieri, who gave geometrical arguments for n=3,4,...,9. Subsequently Wallis, Fermat
From playlist Famous Math Problems
Chebfun is a Matlab-based open-source software project for "numerical computing with functions" based on algorithms related to Chebyshev polynomials. At the 2013 SIAM Annual Meeting, SIAM Past President Nick Trefethen spoke about his activities related to developing Chebfun.
From playlist Complete lectures and talks: slides and audio
16. ODE-IVP and Numerical Integration 4
MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: William Green Topics continued on solving problems of ordinary differential equation with initial value. Also introduced concept of functionals and nest
From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015
Learn how to find the vertex of a parabola
👉 Learn about the parts of a parabola. A parabola is the shape of the graph of a quadratic equation. A regular palabola is the parabola that is facing either up or down while an irregular parabola faces left or right. A quadratic equation is an equation whose highest exponent in the variab
From playlist Find the Parts of a Parabola