Insights into Mathematics | Euclid Book 1 Props I -- V --- a critical review | Sociology and Pure Mathematics | N J Wildberger @njwildberger | Uploaded 3 years ago | Updated 1 hour ago
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??

Video Contents: (thanks to phi Architect)
00:00 Intro
01:20 Elements Book 1 Prop 1 - To describe and Equilateral Triangle upon a given finite Right Line.
04:25 Elements Book 1 Prop 2 - At a given Point, to put a Right Line equal to a Right Line given.
09:14 Elements Book 1 Prop 3 - Two unequal Right Lines being given, to cut off a Part from the great Equal to the lesser.
11:10 Elements Book 1 Prop 4 - Theorem
18:24 Elements Book 1 Prop 5 - Theorem - The Angles at the Base of an Isosceles Triangle are equal between themselves; and if the equal Sides be produced, the Angles under the base shall be equal between themselves.
21:20 Problems (logic) with Euclid so far
25:38 Conclusion


***********************
My research papers can be found at my Research Gate page, at 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 are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at 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 patreon.com/njwildberger Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

youtube.com/playlist?list=PL55C7C83781CF4316
youtube.com/playlist?list=PL3C58498718451C47
youtube.com/playlist?list=PL5A714C94D40392AB
youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw
youtube.com/playlist?list=PL8403C2F0C89B1333
youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa
youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
youtube.com/playlist?list=PL6763F57A61FE6FE8
youtube.com/playlist?list=PLBF39AFBBC3FB30AF
youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW
youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7