Ancient mathematics/History of mathematics

[ConspiracyJim]

TL;DR Summary

I need help understanding the transition from Euclid and Apollonius to Descartes.

Hello,I am trying to teach myself mathematics by starting with Euclid and going up to today. My only background is college algebra and high school algebra and geometry. I am 44 years old.

I've read Euclid and Apollonius. I understood everything except he Appendix in the Conics book (Green Lion Press). I didn't understand how the compounding was being done in the locus problem. I couldn't recall anything Euclid to help me with it.

I tried reading Descartes's Geometry where he deals with the locus problem, but I didn't know if I should continue on if I don't yet understand the compuounding nor Descartes' dealing with the locus problem. I haven't yet read his section on curves.

I have Thomas Heath's History of Greek Mathematics, and I think I should read that before continuing further.

My need, if you could help, is to knownwhat is the best way to prepare for Descartes because I didn't understand much

 

[FactChecker]

I am trying to teach myself mathematics by starting with Euclid and going up to today.

Wow! That is a long way to go about learning mathematics!
IMO, you should consider whether you are more interested in learning the history of mathematics or in learning mathematics itself. The two paths are very different.
For the history of mathematics, I recommend E.T. Bell's Men of Mathematics, and maybe The Math Book by Clifford A Pickover.
For learning mathematics itself, I recommend that you look at the texts for undergrad / graduate mathematics courses, depending on your mathematical background.

 

[PeroK]

Summary:: I need help understanding the transition from Euclid and Apollonius to Descartes.

Hello,I am trying to teach myself mathematics by starting with Euclid and going up to today. My only background is college algebra and high school algebra and geometry. I am 44 years old.

I've read Euclid and Apollonius. I understood everything except he Appendix in the Conics book (Green Lion Press). I didn't understand how the compounding was being done in the locus problem. I couldn't recall anything Euclid to help me with it.

I tried reading Descartes's Geometry where he deals with the locus problem, but I didn't know if I should continue on if I don't yet understand the compuounding nor Descartes' dealing with the locus problem. I haven't yet read his section on curves.

I have Thomas Heath's History of Greek Mathematics, and I think I should read that before continuing further.

My need, if you could help, is to knownwhat is the best way to prepare for Descartes because I didn't understand much

Euclid was brilliant and mathematics isn't medicine, but if you wanted to learn modern medicine, you wouldn't start with the ancient Greeks!

Modern mathematics started in the 1600's with Descartes, Newton, Leibnitz. But even then, the original texts are not to be recommeded. A modern mathematician writing a textbook for today's students knows so much more than even those great minds of the past.

Plus, having a computer at your disposal revolutionises what you can achieve mathematically. I would move straight on to texts for the modern student.

Don't get me wrong, Euclid especially is great as a specialty subject, but geometry has progressed a long way since then.

 

[jedishrfu]

Your quest is daunting. In addition to the other books mentioned here, I’d recommend this book by Gullberg:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

 

[lavinia]

I tried to find Appolonius's proof on line. Can you give a link?

In looking around I saw that there is another problem of Appolonius dealing with tangent circles to three arbitrarily given circles which has spurred a lot of mathematics and has had many different proofs. This video explains a proof that uses only straight edge and compass. This is probably what Appolonius tried to do but maybe with a different approach.



The Greeks tried to solve a variety of problems with straight edge and compass. You might like to play with these problems since they are geometrically intuitive and have inspired a lot of mathematics.

You might also like to go through the some of the many failed historical proofs of Euclid's Parallel Posulate since these too ultimately led to important modern mathematics.

I would also spend a long time on problems in classical Euclidean geometry. Try to prove them yourself before reading a proof. IMO learning Mathematics is learning how to think mathematically. One can not do this without struggling with proofs on one's own.

 

[ConspiracyJim]

Wow! That is a long way to go about learning mathematics!
IMO, you should consider whether you are more interested in learning the history of mathematics or in learning mathematics itself. The two paths are very different.
For the history of mathematics, I recommend E.T. Bell's Men of Mathematics, and maybe The Math Book by Clifford A Pickover.
For learning mathematics itself, I recommend that you look at the texts for undergrad / graduate mathematics courses, depending on your mathematical background.

Hello,

Thank you for the suggestions.

I have seen two of Bell's book, but that's not what I need. It is the mathematics itself that I'm interested in. I just want to learn how math actipually developed, and then learn how it was applied to nature. I understand the philosphical side playsna part, too.

Thanks.

 

[ConspiracyJim]

Euclid was brilliant and mathematics isn't medicine, but if you wanted to learn modern medicine, you wouldn't start with the ancient Greeks!

Modern mathematics started in the 1600's with Descartes, Newton, Leibnitz. But even then, the original texts are not to be recommeded. A modern mathematician writing a textbook for today's students knows so much more than even those great minds of the past.

Plus, having a computer at your disposal revolutionises what you can achieve mathematically. I would move straight on to texts for the modern student.

Don't get me wrong, Euclid especially is great as a specialty subject, but geometry has progressed a long way since then.

Hello,

Thanks for the suggestions, but I'm trying to understand the development of mathematics, and how people made discoveries.

Also, when I ws in high school, we were taught the pythagorian theorem, but we didn't have a clipue from where it was derived. Math was just the memorization of formulas. But when I first read Euclid, I realized where those formulas in geometry class came from. Likewise, reading Apollonius gave me an understanding of conic sections that I never read in a modern textbook. Although I haven't finished Descartes because I'm stuck on something, I can see how he will take geometry and combinenit with algebra, and then I will understand better the concepts behind the formulas.

Maths sucks when it's just a bunch of formulas with no concepts. I'm a layman and not a physicist. I came to this in the hope that someone could me to understand the concepts behind the science.

As others have said, "We stand on the shoulders of giants."

 

[ConspiracyJim]

Your quest is daunting. In addition to the other books mentioned here, I’d recommend this book by Gullberg:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

Hello,

Thank you for the suggestion. Do you know if the book teaches the subject from the modern point of view, and using modern mathematical notation? I onky have algebra 2 knowledge.

Thank you.

 

[PeroK]

Hello,

Thanks for the suggestions, but I'm trying to understand the development of mathematics, and how people made discoveries.

Also, when I ws in high school, we were taught the pythagorian theorem, but we didn't have a clipue from where it was derived. Math was just the memorization of formulas.

The history of mathematics is a fascinating subject in its own right. Why mathematics is taught the way it is in schools is sad, but most modern textbooks on mathematics emphasise understanding.

You don't have to go back to the ancients to get a full explanation of conic sections, for example.

 

[PeroK]

Ps you could do an Internet search for "proof of pythagoras" and see what that turns up!

 

[jedishrfu]

Yes Gullberg's book uses modern notation with many sidebars on math history. I think amazon has a look inside feature so you can see what its like to read. In the preface, Dr Gullberg says he wrote it to help his son in college.

 

[neilparker62]

As others have said, "We stand on the shoulders of giants."

https://www.goodreads.com/book/show/32610.On_the_Shoulders_of_Giants

If you read the Copernican section, you'll find some interesting geometry in "Liber Primus". (Book One).