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tech / sci.math / 7 September: New visitors to sci.math: The exactness of measure in geometry: Constructing a line equal to the circumference of a given circle.

7 September: New visitors to sci.math: The exactness of measure in geometry: Constructing a line equal to the circumference of a given circle.

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Subject: 7 September: New visitors to sci.math: The exactness of measure in
geometry: Constructing a line equal to the circumference of a given circle.
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Wed, 7 Sep 2022 14:43 UTC

What the astute student will realise from Propositions 18 and 19 of spiral besides the exactness of measure in geometry, is that if Ancient Greeks thought of a tangent line in the same way as the incorrigible fools of today and the last few hundred years, this knowledge (*) would never have been realised.

(*) Given any circle, a line with the same length as its circumference can be constructed. Conveniently, it is not even necessary to construct a spiral but to put to use the properties that are known therefrom and thus determine such a straight line.

Ο νόων νόειτω.

Find me on Academia.edu where you will learn more than you have in all your school and university years.

Re: 7 September: New visitors to sci.math: The exactness of measure in geometry: Constructing a line equal to the circumference of a given circle.

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Subject: Re: 7 September: New visitors to sci.math: The exactness of measure
in geometry: Constructing a line equal to the circumference of a given circle.
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Wed, 7 Sep 2022 14:46 UTC

On Wednesday, 7 September 2022 at 07:43:45 UTC-7, Eram semper recta wrote:
> What the astute student will realise from Propositions 18 and 19 of spiral besides the exactness of measure in geometry, is that if Ancient Greeks thought of a tangent line in the same way as the incorrigible fools of today and the last few hundred years, this knowledge (*) would never have been realised.
>
> (*) Given any circle, a line with the same length as its circumference can be constructed. Conveniently, it is not even necessary to construct a spiral but to put to use the properties that are known therefrom and thus determine such a straight line.
>
> Ο νόων νόειτω.
>
> Find me on Academia.edu where you will learn more than you have in all your school and university years.

These propositions are part of Archimedes' work On Spirals.

Re: 7 September: New visitors to sci.math: The exactness of measure in geometry: Constructing a line equal to the circumference of a given circle.

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Subject: Re: 7 September: New visitors to sci.math: The exactness of measure
in geometry: Constructing a line equal to the circumference of a given circle.
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by: Quantum Bubbles - Wed, 7 Sep 2022 17:31 UTC

On Wednesday, September 7, 2022 at 3:43:45 PM UTC+1, Eram semper recta wrote:

> Find me on Academia.edu where you will learn more than you have in all your school and university years.

How would you know JG115? If memory serves you didn't successfully complete your maths degree?

All studying your work for any significant length of time shows is the crippling consequences of letting ego exceed rationality, and the importance of sticking to good, well reviewed university textbooks. Textbooks, such as:

Calculus: a Complete Course, 9th ed, by Adams & Essex

Real Mathematical Analysis, 2nd ed, by Pugh

Elementary Differential Geometry, 2nd ed, by Pressley

just for starters.

Regards

QB 133
Remain Calm and Keep Loving Differential Geometry

Subject	Author
7 September: New visitors to sci.math: The exactness of measure in	Eram semper recta
Re: 7 September: New visitors to sci.math: The exactness of measure	Eram semper recta
Re: 7 September: New visitors to sci.math: The exactness of measure	Quantum Bubbles