Verifying Archimedes' parabolic area formula with Algebraic Calculus | AC and DCB Curves 5| Wild Egg

The Algebraic Calculus One course, available now online at openlnearing, gives a novel and more algebraic approach to the subject, where curves take precedence over functions, where limits and real numbers are not required, and where the logical structure is clear, happily with no cheating. The connections with geometry and linear algebra become more evident, and there are now dozens of challenging directions to explore in, including this series concentrating on the de Casteljau Bezier (dCB) curves.

In this lecture we summarize some of the basic notions and results of the Algebraic Calculus.

As an illustration of the power of this new approach, we show how to verify in a special case Archimedes' remarkable parabolic area formula valid for a general parabola in the plane --- something that classical Calculus struggles to do. For us we capture this geometric situation using the idea of a quadratic dCB curve. We will crucially be using the Fundamental theorem in the Algebraic Calculus -- which is quite different from the "Fundamental theorem" you might be used to!

While not a solid introduction to the Algebraic Calculus, this video will give you enough of an introduction that with some work you can go through the argument and understand it quite well. And then you will be prepared as we move into exciting uncharted waters with cubics and beyond!

Please consider becoming a Member of the Wild Egg Maths (YouTube) channel at https://www.youtube.com/channel/UCriFv3G22iOUidUhkIGXuhw to access all the videos that will be posted in this series, along with notable others. Including how to solve general polynomial equations, and how to create exceptional structures in mathematics and physics through dynamics on graphs, and advice on being an amateur mathematician, or a graduate student in the subject. Also extra pdf and worksheet resources will be available to Members there. Lots to learn and do, so please join us. :)

And the exciting Algebraic Calculus One online course is now open at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects. Dozens of rich hours or learning and activity await you with this novel, powerful and beautiful treatment.

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger

My blog is at http://njwildberger.com/, where I discuss lots of foundational issues, along with other things.

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated. :)

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Видео Verifying Archimedes' parabolic area formula with Algebraic Calculus | AC and DCB Curves 5| Wild Egg канала Insights into Mathematics