Question

I am neither a mathematician nor a maths major student. More likely, I am a dumb person in mathematics especially in three- dimensional geometry. I can’t draw an acceptable diagram and apply theorem to proof any questions in my homework. I tried to find a way to became an “average person”, but I failed. My question is : are there any books , videos o, classes in college or whatever start to talk about some basic problems in three- dimentional geometry and develop the basic understanding of it? I don’t need any answer like “ I am sorry that’s so bad” or “there are some courses in college talking about geometry, such as 304 or 415.” I am hearing these for years! The question seems quite weird posting here. Give me your suggestions if you don’t mind to reduce your maths taste.

Answer 1

I'm not sure what you mean with three-dimensional geometry, but if you mean geometry of curves and surfaces in $\mathbb{R}^3$ I would recommend you

Differential Geometry of Curves and Surfaces, by Manfredo Do Carmo .

Answer 2

I'm guessing wildly here, but it sounds like you are having difficulty translating between algebraic manifestations of a concept (like with equations) and geometric representations (such as with pictures, or the general idea of objects in space). I don't have any silver-bullet answers, since I also had trouble picking up these sorts of questions.

There are some online resources listed at mathforum.org, and I would also recommend looking at Project MATHEMATICS and The Geometry Center. I don't know how appropriate these are for you, since I'm unable to ascertain your math background. Try not to get too discouraged if something is pitched too high.

I have an off-the-wall suggestion: if you can take an art class that emphasizes perspective studies (perhaps while reading a math book on projective geometry), it might help your visualization skills. It can be beneficial to focus intensively on exactly how the different ways of viewing an object will change the way it appears.