Recent content by Noxide

Please explain the difference between these two statements. 1 + 2 + ... + n = 1/2n(n+1) for all n in the natural numbers 1 + 1/2 + 1/4 + ... + 1/2^n = 2 - 1/2^n for all n in the natural numbers Why does the first explicitly show two terms being summed whereas the second shows 3 terms...

A little clarification is required for the following techniqueTHE TECHNIQUE Given a surface z = f(x,y), and some point Q in R3 (not on the surface) The point P on the surface for which the distance from P(x, y, f(x,y)) to Q is the shortest distance from the surface to Q (i.e. vector PQ has...

I wouldn't worry about the calculus aspect of calc 3, having a solid base in linear algebra will do you much more good in a multivariable course than any memorized identity or procedure related to calc 1 or 2

Having seen your alternate explanation and proof, I am curious for which situations the above reasoning can be applied. Would this be considered logically sound in a formal proof (using limit arguments) or is this just an intuitive explanation? I fear that my inability to decipher this problem...

:approve: Thank you!

I know that that statement is true, but only because my text states it, however my text does not explain why it is true. If you could explain why it is true or give me a theorem that would help, I would greatly appreciate it.

I see that angle ACB is half of arc AB. But I don't see why we can also say that angle LAB is congruent to ACB because LAB is measured from half of arc AB (which is the reason my textbook gives for the congruence of ACB and LAB).

Hmm. I don't think I know how to get that angle BAL is congruent to angle C afterall...

Triangle ABC is any triangle. My book says it's because both angles are measured from half of arc AB but I don't see how they can say that.

Why does angle LAB = angle ACB? line AL is tangent to the circle at A Triangle ABC is inscribed in the circle http://img13.imageshack.us/img13/9553/tricircle.png Uploaded with ImageShack.us

Hmm. I don't know if that one applies here. My geometry is really weak and I would appreciate any possible insight. I'll add the image below. Notice that L is a proper Cevian. http://img13.imageshack.us/img13/9553/tricircle.png Uploaded with ImageShack.us

I will preface this by saying that if anyone has the following book: Euclidean Geometry and Transformations written by Clayton W. Dodge, then my question concerns a theorem used but unstated in the proof of Theorem 4.5. Theorem 4.5 The lines tangent to the circumcircle of a triangle at its...

I need help finding a solid introductory book on finance. I know nothing about finance other than its definition on wikipedia and I want to learn more. Can anyone recommend a solid text that starts from the most fundamental concepts and definitions and works its way up?

English sentences are used to communicate ideas in mathematical research papers. Sentences only make sense given that they follow rules of syntax. Linguistics helps one to understand and apply rules of syntax to english sentences. In case you forgot, english (a natural language) sentences are...

As many of you know, precise language is necessary for effective communication in mathematics. Although I find that I am quite capable of communicating my thoughts effectively and clearly, I feel that there is always room for improvement. Please recommend an introductory, and perhaps a...