Are there any good books on logic and plane geometry?

In summary, the conversation discusses book recommendations for logic and plane geometry. The individual is looking for books that combine logic with analysis and mentions "How to Prove It" by Daniel J Velleman as a reference. They also mention their interest in mathematical logic and ask for specific recommendations. The conversation concludes with suggestions for Ebbinghaus, Monk, Shoenfield, J.L. Bell, and "A friendly introduction to mathematical logic" by Chris Leary.
  • #1

After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane geometry. The subjects aren't related, I just wanted to combine them into one post :P

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  • #2
Logic paired with analysis. What does that mean? Logic has very little to do with analysis. So I fear there won't be much books that combine the two topics.
What kind of logic do you want anyway?? Do you want things like truth tables and stuff (basically what Velleman does)? Or do you want real mathematical logic?? If you want mathematical logic, then I highly recommend Ebbinghaus.

What do you mean with "plane geometry"?? Do you want a high school text?? A university level text?? Here are some books you could try:

- Euclid' Elements: The classic book on plane geometry. I'd still recommend it to people if they want to learn classic geometry. It won't get into analytical geometry like equations of lines.

- Geometry by Serge Lang: this is high school geometry done on college level. It focuses on equations of lines and so on. Serge Lang is an excellent writer, so the book is highly recommended.

- Introduction to geometry by Coxeter: if you know high school geometry well, then this is the book for you. It is basically a survey of all of mathematical geometry. It even introduces things like differential geometry and algebraic geometry.
  • #3
you're right, I was rather vague.

I'm looking to steer away from the pure logic and move into mathematical logic. So Ebbinghaus?

Perfect, thank you very much.
  • #4
"mathematical logic" is quite different from what you might expect ( it will be nothing like "how to prove it" ). For example, in mathematical logic, you will learn about the consequences of having a "theory" ( imagine I develop a theory describing physical phenomena, will I be able to derive contradictions? can I *really* describe everything that can possibly happen? ).
Another thing that may be a consequence of having a theory, is that you may be able to generate all the theorems ( imagine with a computer ) possible ( plane geometry can do this ). Or, if you are given a statement, can you in general decide whether or not this statement follows from your theory? ( or, provide a method that will help you check ).

Anyway, good mathematical logic texts I think ( for the general logic level) are: Ebbinghaus, Monk, Shoenfield and J.L. Bell.

A good book that is less dry and is a lighter read is "A friendly introduction to mathematical logic" by Chris Leary.
  • #5

There are many good books on logic and plane geometry available. Some popular options include "Euclid's Elements" by Euclid, "A Concise Introduction to Logic" by Patrick J. Hurley, and "Introduction to Geometry" by Richard Rusczyk and David Patrick. It's always a good idea to read reviews and ask for recommendations from others who have read these books to find the one that best suits your needs and interests. Happy reading!

1. What is plane geometry?

Plane geometry is a branch of mathematics that deals with the properties and relationships of geometric figures on a two-dimensional plane.

2. What are the basic elements of plane geometry?

The basic elements of plane geometry include points, lines, angles, and shapes such as triangles, circles, and squares. These elements can be used to construct more complex figures and solve geometric problems.

3. How is logic used in plane geometry?

Logic is an important tool in plane geometry as it helps us to make logical deductions and prove geometric theorems. It involves using reasoning and mathematical principles to make conclusions about geometric figures and their properties.

4. Can you explain the difference between deductive and inductive reasoning in plane geometry?

Deductive reasoning in plane geometry involves starting with a general premise or rule, and using logic to draw specific conclusions. Inductive reasoning, on the other hand, involves making observations and using them to form a general rule or hypothesis.

5. How is plane geometry applied in real life?

Plane geometry has many practical applications, such as in architecture, engineering, and design. It is used to create accurate maps, design buildings and structures, and solve real-world problems involving shapes and measurements.

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