Reddit Reddit reviews Kiselev's Geometry, Book I. Planimetry

We found 6 Reddit comments about Kiselev's Geometry, Book I. Planimetry. Here are the top ones, ranked by their Reddit score.

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6 Reddit comments about Kiselev's Geometry, Book I. Planimetry:

u/jacobolus · 4 pointsr/math

I’m not sure precisely what you mean by “contemporary” or “geometric algebra” or “basic number elements and algebra”. What did you feel was missing from Lang’s book? (I’m not familiar with its contents.)

If you want something in line with the standard high school curriculum, but maybe a bit more rigorous than most, this book by Kiselev was the standard Russian school text for generations (review)

Or you could try the Art of Problem Solving geometry book (site).

There’s a lot of good stuff in Coxeter and Greitzer’s book Geometry Revisited, but I’d say it probably assumes a standard high school geometry course as a prerequisite.

Not really limited to plane geometry, but I really like Hilbert and Cohn-Vossen’s book Geometry and the Imagination (review). I’d recommend getting a used copy of the original printing; the recent ones are printed on demand and not as nice.

Also let me recommend Apostol and Mamikon’s lovely book New Horizons in Geometry (review), though it’s more about calculus than algebra per se.

If you want to study plane curves from a complex number perspective, you could try Zwikker’s 1963 The advanced geometry of plane curves and their applications

If by geometric algebra you mean Grassmann/Clifford/Hestenes style algebra, check out the stuff Jim Smith has been doing, or you could take a look at this thing (I haven’t read it), or try these papers.

They probably aren’t what you’re looking for, but I think Farouki’s Pythagorean Hodograph Curves are pretty neat (that book also has a lot of other interesting material in it). Also neat for formalistic theorizing about algebras for spline curves is Ramshaw’s monograph On Multiplying Points: The Paired Algebras of Forms and Sites (probably a bit abstract for what you want here).

What are your goals? Do you want to design lenses and mirrors for cameras? Model classical mechanics systems? Construct arbitrary shapes out of polynomial curves so you can draw fonts or animate characters on a computer screen? Design cut paths for CNC machines? Approximate transcendental functions by some type of function that you can more easily compute with? Find the prettiest proofs of thousand-year-old theorems about circles? Prepare yourself to study differential geometry or algebraic topology? ...

u/ur_mom415 · 2 pointsr/UBC

Read this: https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 and you're more than set for algebraic manipulation.

And if you're looking to get super fancy, then some of that: https://www.amazon.com/Method-Coordinates-Dover-Books-Mathematics/dp/0486425657/

And some of this for graphing practice: https://www.amazon.com/Functions-Graphs-Dover-Books-Mathematics/dp/0486425649/

And if you're looking to be a sage, these: https://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202/ + https://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210/

If you're uncomfortable with mental manipulation of geometric objects, then, before anything else, have a crack at this: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/

u/hihoberiberi · 1 pointr/learnmath

I took a geometry course a couple of quarters ago that was sort of a review of high school geometry, except rigorous and proof-oriented. According to my prof, Kiselev's Geometry is the absolute best book available for this approach to the subject.

u/dp01n0m1903 · 1 pointr/math

This has turned out to be a much more interesting question than I had thought it would be. It seems to be unexpectedly hard to find a good, short book on Euclidean geometry. Most of the really good books are advanced treatments that have a lot more to say than what you probably want. Anyway, there is a good discussion of this question on mathoverflow. It appears that Kiselev is a pretty good choice. Hartshorne might be good as a guide to learning straight from Euclid (and lots more besides). I don't know how far you really want to go with this project. It might be enough to just get a taste of how the whole synthetic geometry program is organized.

By the way, you know about libary.nu, right?

u/Newblik · 1 pointr/learnmath

I've heard people recommend Kiselev's Geometry, on a physics forum. Warning, though; Kiselev's Geometry series(in English) is translated from Russian.

Here's the link to where I got all these resources(I also copy-pasted what's in the link down below; although, I did omit a few entries, as it would be too long for this reddit comment; click the link to see more resources):

https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/

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Note: Alternatively, you can order Kiselev's geometry series from http://www.sumizdat.org/

Geometry I and II by Kiselev


http://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202

http://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210

> If you do not remember much of your geometry classes (or never had such class), then you can hardly do better than Kiselev’s geometry books. This two-volume work covers a lot of synthetic (= little algebra is used) geometry. The first volume is all about plane geometry, the second volume is all about spatial geometry. The book even has a brief introduction to vectors and non-Euclidean geometry.

The first book covers:

  • Straight lines

  • Circles

  • Similarity

  • Regular polygons and circumference

  • Areas

    The second book covers:

  • Lines and Planes
  • Polyhedra
  • Round Solids
  • Vectors and Foundations

    > This book should be good for people who have never had a geometry class, or people who wish to revisit it. This book does not cover analytic geometry (such as equations of lines and circles).

    ____

    Geometry by Lang, Murrow


    http://www.amazon.com/Geometry-School-Course-Serge-Lang/dp/0387966544

    > Lang is another very famous mathematician, and this shows in his book. The book covers a lot of what Kiselev covers, but with another point of view: namely the point of view of coordinates and algebra. While you can read this book when you’re new to geometry, I do not recommend it. If you’re already familiar with some Euclidean geometry (and algebra and trigonometry), then this book should be very nice.

    The book covers:

  • Distance and angles

  • Coordinates

  • Area and the Pythagoras Theorem

  • The distance formula

  • Polygons

  • Congruent triangles

  • Dilations and similarities

  • Volumes

  • Vectors and dot product

  • Transformations

  • Isometries

    > This book should be good for people new to analytic geometry or those who need a refresher.

    > Finally, there are some topics that were not covered in this book but which are worth knowing nevertheless. Additionally, you might want to cover the topics again but this time somewhat more structured.

    > For this reason, I end this list of books by the following excellent book:

    Basic Mathematics by Lang


    http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877

    > This book covers everything that you need to know of high school mathematics. As such, I highly advise people to read this book before starting on their journey to more advanced mathematics such as calculus. I do not however recommend it as a first exposure to algebra, geometry or trigonometry. But if you already know the basics, then this book should be ideal.

  • The book covers:

  • Integers, rational numbers, real numbers, complex numbers

  • Linear equations

  • Logic and mathematical expressions

  • Distance and angles

  • Isometries

  • Areas

  • Coordinates and geometry

  • Operations on points

  • Segments, rays and lines

  • Trigonometry

  • Analytic geometry

  • Functions and mappings

  • Induction and summations

  • Determinants

    > I recommend this book to everybody who wants to solidify their basic knowledge, or who remembers relatively much of their high school education but wants to revisit the details nevertheless.

    _____

    More links:

    https://math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry

    Note: oftentimes, you can find geometry book recommendations( as well as other math book recommendations) in stackexchange; just use the search bar.

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    https://www.physicsforums.com/threads/geometry-book.727765/

    https://www.physicsforums.com/threads/decent-books-for-high-school-algebra-and-geometry.701905/

    https://www.physicsforums.com/threads/micromass-insights-on-how-to-self-study-mathematics.868968/
u/Mukhasim · 1 pointr/math

To add to my last paragraph, if you wanna go even more basic, you can get a pre-algebra textbook. That's basically a review of everything in the standard US K-7 curriculum. A reasonable reference book for this is Yang's A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1.

For the impatient, look at these three books (I use Amazon links here but I don't care where you buy them):