Euclid Book 1 Props I -- V --- a critical review | Sociology and Pure Mathematics | N J Wildberger
Modern pure mathematics is based largely on the historically vital example of Euclid, in particular the first Books of his classic work The Elements. Even non-mathematical people can gain an understanding of the logical orientation of the subject by looking carefully at some of the early Propositions in Book I, which is what we do here. We look at Props I --- V, and explain what Euclid is trying to do and how he sets out doing this.
Constructions play an important role, using both the straight-edge (a ruler without markings) and a compass. However there are also purely theoretical results, for example the first Theorem of Prop IV, which gives the famous side-angle-side congruence condition, but stated in a rather laborious way.
In order to understand this, we will have to discuss the role of angle in Euclidean geometry, which notably did not involve the Babylonian angle measurement system (or any other angle measurement system).
And then we are in a position to ask some serious questions about the logical validity of Euclid, especially when regarded as a foundation for modern geometry. Could it be that Euclid was really more of an applied mathematician??
*****************
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 will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
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.
Видео Euclid Book 1 Props I -- V --- a critical review | Sociology and Pure Mathematics | N J Wildberger канала Insights into Mathematics
Constructions play an important role, using both the straight-edge (a ruler without markings) and a compass. However there are also purely theoretical results, for example the first Theorem of Prop IV, which gives the famous side-angle-side congruence condition, but stated in a rather laborious way.
In order to understand this, we will have to discuss the role of angle in Euclidean geometry, which notably did not involve the Babylonian angle measurement system (or any other angle measurement system).
And then we are in a position to ask some serious questions about the logical validity of Euclid, especially when regarded as a foundation for modern geometry. Could it be that Euclid was really more of an applied mathematician??
*****************
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 will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
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.
Видео Euclid Book 1 Props I -- V --- a critical review | Sociology and Pure Mathematics | N J Wildberger канала Insights into Mathematics
Показать
Комментарии отсутствуют
Информация о видео
28 февраля 2021 г. 11:17:19
00:28:49
Другие видео канала
Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J WildbergerEuclid Book 1 Props VI-VIII - a foundation for geometry | Sociology and Pure Maths | N J WildbergerInfinities and Skepticism in Mathematics: Steve Patterson interviews N J WildbergerNon-Euclidean geometry | Math History | NJ WildbergerWhy π^π^π^π could be an integer (for all we know!).Coin, Cash and Credit, and Fractional Reserve Banking | Wild West Banking | N J WildbergerProjective geometry | Math History | NJ WildbergerGreek geometry (a) | Math History | NJ WildbergerInfinity: does it exist?? A debate with James Franklin and N J WildbergerWhy the World’s Best Mathematicians Are Hoarding ChalkThe remarkable Dihedron algebra | Famous Math Problems 21b | N J WildbergerHow to set up fractions IV: the relation between fractions and other number systems | FMP24d | NJWA Systematic Approach to Logical Deduction & the Boole-Mobius Transform I | MF 277 | N J WildbergerDebt, Bonds and Default | Wild West Banking | N J WildbergerInventing Game of Life (John Conway) - NumberphileThe Banach Tarski paradox - is it nonsense? | Sociology and Pure Mathematics | N J WildbergerThe true role of the circular functions | WildTrig: Intro to Rational Trigonometry | N J WildbergerHow to set up fractions III - canonical forms via the Euclidean Algorithm | FamousMathProbs24c | NJWThe rational number line and irrationalities (b) | Famous Math Problems 19b | NJ Wildberger