Apollonius' circle construction problems | Famous Math Problems 3 | NJ Wildberger
30.2 هزار بار بازدید -
12 سال پیش
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Around 200 B.C., Apollonius of
Around 200 B.C., Apollonius of Perga, the greatest geometer of all time, gave a series of related problems; how to construct a circle in the plane touching three objects, where the objects are either a point (P), a line (L) and or a circle (C). Many mathematicians have studied this most famous of all geometric problems.
In this video we give some of the history, discuss Euclid's solution to two of the problems (which predate Apollonius' work), and summarize some circle geometry that is relevant to the subject: the Subtended spreads theorem from Rational Trigonometry, the power of a point wrt a circle, the pole-polar duality determined between points and lines by a circle, and inversion.
We also discuss the importance of constructions in both education and theoretical work---a point which has gradually been diminished over the years. Modern mathematics can learn a lot by re-thinking its attitude to the existence of mathematical objects by understanding the clarity that arises from the ancient Greek, and 17th and 18th century insistence on explicit constructions.
This problem has aspects which range in difficulty from 1 to 5. It is a great challenge for aspiring geometers.
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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/...
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/... 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: njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: playlist
list=PL8403C2F0C89B1333
Year 9 Maths: Year9Maths
Ancient Mathematics: Ancient Mathematics
Wild West Banking: Wild West Banking
Sociology and Pure Mathematics: Sociology and Pure Mathematics
Old Babylonian Mathematics (with Daniel Mansfield): playlist
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: MathHistory: A course in the History ...
Wild Trig: Intro to Rational Trigonometry: WildTrig: Intro to Rational Trigonometry
MathFoundations: Math Foundations
Wild Linear Algebra: Wild Linear Algebra
Famous Math Problems: Famous Math Problems
Probability and Statistics: An Introduction: Probability and Statistics: an introd...
Boole's Logic and Circuit Analysis: Boole's Logic and Circuit Analysis
Universal Hyperbolic Geometry: Universal Hyperbolic Geometry
Differential Geometry: Differential Geometry
Algebraic Topology: Algebraic Topology
Math Seminars: MathSeminars
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: ENCYCLOPEDIA OF TRIANGLE CENTERS
Six: An elementary course in pure mathematics: Six: An elementary course in Pure Mat...
Algebraic Calculus One: Algebraic Calculus One
Algebraic Calculus Two: Algebraic Calculus Two
м
In this video we give some of the history, discuss Euclid's solution to two of the problems (which predate Apollonius' work), and summarize some circle geometry that is relevant to the subject: the Subtended spreads theorem from Rational Trigonometry, the power of a point wrt a circle, the pole-polar duality determined between points and lines by a circle, and inversion.
We also discuss the importance of constructions in both education and theoretical work---a point which has gradually been diminished over the years. Modern mathematics can learn a lot by re-thinking its attitude to the existence of mathematical objects by understanding the clarity that arises from the ancient Greek, and 17th and 18th century insistence on explicit constructions.
This problem has aspects which range in difficulty from 1 to 5. It is a great challenge for aspiring geometers.
************************
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/...
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/... 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: njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: playlist
list=PL8403C2F0C89B1333
Year 9 Maths: Year9Maths
Ancient Mathematics: Ancient Mathematics
Wild West Banking: Wild West Banking
Sociology and Pure Mathematics: Sociology and Pure Mathematics
Old Babylonian Mathematics (with Daniel Mansfield): playlist
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: MathHistory: A course in the History ...
Wild Trig: Intro to Rational Trigonometry: WildTrig: Intro to Rational Trigonometry
MathFoundations: Math Foundations
Wild Linear Algebra: Wild Linear Algebra
Famous Math Problems: Famous Math Problems
Probability and Statistics: An Introduction: Probability and Statistics: an introd...
Boole's Logic and Circuit Analysis: Boole's Logic and Circuit Analysis
Universal Hyperbolic Geometry: Universal Hyperbolic Geometry
Differential Geometry: Differential Geometry
Algebraic Topology: Algebraic Topology
Math Seminars: MathSeminars
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: ENCYCLOPEDIA OF TRIANGLE CENTERS
Six: An elementary course in pure mathematics: Six: An elementary course in Pure Mat...
Algebraic Calculus One: Algebraic Calculus One
Algebraic Calculus Two: Algebraic Calculus Two
м
12 سال پیش
در تاریخ 1391/11/04 منتشر شده
است.
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