Science for Everyone – Problems in Solid Geometry

We are still on the Science for Everyone series. This post is first of two books by I. F. Sharygin. The two books are problem and solution books in geometry. In this post the Problems in Solid Geometry is taken up. The next post would be Problems in Plane Geometry.

From the Preface:

This book contains 340 problems in solid geometry and is a natural continuation of Problems in Plane Geometry, Nauka, Moscow, 1982. It is therefore possible to confine myself here to those points where this book differs from the first. The problems in this collection are grouped into (1) computational problems and (2) problems on proof.

The simplest problems in Section 1 only have answers, others, have brief hints, and the most difficult, have detailed hints and worked solutions. There are two reservations. Firstly, in most cases only the general outline of the solution is given, a number of details being suggested for the reader to consider. Secondly, although the suggested solutions are valid, they are not patterns (models) to be used in examinations. Sections 2-4 contain various geometric facts and theorems, problems on maximum and minimum (some of the problems in this part could have been put in Section 1), and problems on loci. Some questions pertaining to the geometry of tetrahedron, spherical geometry, and so forth are also considered here.

As to the techniques for solving all these problems, I have to state that I prefer analytical computational methods to those associated with plane geometry. Some of the difficult problems in solid geometry will require a high level of concentration from the reader, and an ability to carry out some rather complicated work.

The book was translated from the Russian by Leonid Levant and was first published by Mir in 1986.

All credits to the original uploader.

Update Jan 2020

The Internet Archive Link

Contents are as under:

Preface 6
Section 1. Computational Problems 7
Section 2. Problems on Proof 37
Section 3. Problems on Extrema. Geometric
Inequalities 47
Section 4. Loci of Points 54
   An Arbitrary Tetrahedron 59.
   An Equifaced Tetrahedron 61.
   An Orthocentric Tetrahedron 64.
   An Arbitrary Polyhedron.
   The Sphere 65.
An Outlet into Space 68.
Answers, Hints, Solutions 69

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10 Responses to Science for Everyone – Problems in Solid Geometry

  1. Ahmed says:

    Remarkable, I don’t know what I can say to thank you.
    Can you please a list of mir books.


  2. Ahmed says:

    Dear Damitr;

    Thank you again
    here is collection of mir books in Arabic(, or if you want scientific book see this , however isn’t complete collection there some books are not there .
    I will do what can i do.
    Samples form collection:
    Physics for Entertainment (
    In search of beauty(

    sorry my english isn’t prefect.


    • Khalid says:

      Dear Ahmed,

      Thank you for those links!

      I would like to buy leftovers of Smirnov’s “Course of Higher Mathematics” in Arabic, as well as some of Landau’s books presented by Damitr in his useful site.

      Do you know where I could find Mir books in Arabic for sale, in the internet or in a store?
      I only know the site and I discovered your links.

      Thx a lot,


  3. Ashish says:

    Continue with the good work damitr…Can u please provide a link to s s krotov’s aptitude problems in physics(this book is considered the bible for cracking tough physics examinations).Me and my friends searched all over the markets in lucknow even the second hand bookstores in lucknow for this book but all in vain…….I have a book of mir publishers titled Trigonometric Functions: A Problem Solving Approach by A Panchieskin and can upload it on if you wish. Please kindly upload the krotov book as soon as possible if you have it. My physics preparation for IITJEE are at end and want to refine it using this book. I and a lot of my friends will be ver thankful to you. Thank you in advance.


  4. m95 says:

    link is dead, could you please update it?


  5. Nilay says:

    link is not working… the 4shared link is for problems in plane geometry not for solid geometry


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