Math History Questions (MTH105)

[Blue Leader]

Greetings,

I hope that this is the correct place to put these questions. I can't really find any section of the forum that would particularly fit this...

Anyhow, I'm currently in a college math class (MTH-105) where we basically just go over the history of math and mathematicians, and don't usually do any math problems.
I'm trying to finish some homework for the class but I'm a bit stuck on a few of the questions. Out of 36 questions I have just a few that I'm stuck on, and I was wondering if anyone would be able to help me out or point me in the right direction? I cannot find the answers for these questions despite my efforts to seek them out online and in the textbook.

1. Find the digit in the thirtieth decimal place of the decimal expansion of the number e that is the base of the natural logarithms.
After searching around online I've found answers that go up to around the tenth decimal place, but nothing that goes up any where close to the thirtieth place. And I'm not really sure how I'd calculate it... I've read about it, but I just don't get it...

2. What is the fractal dimension of Cantor's Middle Thirds set?
I don't entirely understand this question, and I can't find the solution in my book or searching online, so I'm not entirely sure what I'm doing or what I'm looking for. I have no idea how to answer this question...
Is it some kind of equation I have to solve?

3. Suppose that a planar graph has 97 vertices and 132 faces. How many edges must it have?
Once again... I have no clue what to do with this. I don't even know how to begin solving this thing. In class we just skimmed over planar graphs and I'm still pretty confused about the subject...

And that's it. Any help would be much appreciated.
Thank you for your time!

[stapel_eliz]

1. Find the digit in the thirtieth decimal place of the decimal expansion of the number e that is the base of the natural logarithms.

What method(s) did they give you for finding the value of ? (If none, then look further for decimal expansions of the value.)

2. What is the fractal dimension of Cantor's Middle Thirds set?

I have no idea how to answer this question

If your class hasn't covered this set or fractals, then I see no way for you to answer this. You'd need to spend some weeks studying fractals and infinite series, for a start. Sorry.

3. Suppose that a planar graph has 97 vertices and 132 faces. How many edges must it have?
Once again... I have no clue what to do with this.

I'm sorry to hear that your instructor and your book have not covered the information necessary to answering your homework exercises. Unfortunately, it is not reasonably feasible to attempt to teach a graph theory class in a forum posting. If they haven't given you the definitions and the basic formula for this, then I don't see how they're expecting you to answer this. Sorry.

[Blue Leader]

Thank you for your help. You've actually been the kindest and most understanding person in the few places I posted my questions. The other two forums just basically insulted me for not being able to solve the problems myself.

What method(s) did they give you for finding the value of ? (If none, then look further for decimal expansions of the value.)

Ah, thank you. I tried searching on Google but maybe I just wasn't searching for the correct terms.
I think I was able to find something that helped me, though. If I did it right... I think it's 2...

If your class hasn't covered this set or fractals, then I see no way for you to answer this. You'd need to spend some weeks studying fractals and infinite series, for a start. Sorry.

We usually just skim over most subjects so I don't always understand them... especially because I'm an extremely slow learner. And class is only less than two hours so we don't have much time to go over things. I know we're supposed to read it in our textbook but that doesn't help much if even the textbook doesn't make much sense, heh.
But again, thank you. I think I might have found it now... It looks like, if I'm doing the right thing, that the answer would be log(2)/log(3)...

I'm sorry to hear that your instructor and your book have not covered the information necessary to answering your homework exercises. Unfortunately, it is not reasonably feasible to attempt to teach a graph theory class in a forum posting. If they haven't given you the definitions and the basic formula for this, then I don't see how they're expecting you to answer this. Sorry.

Yeah, like I mentioned, the instructor just tends to skim over topics in the time allotted. While I found some notes on the equation I wasn't thinking lastnight and didn't realize how simple it was to solve it. It was just simple addition and subtraction... Heh, I felt like an idiot after I realized that (which on the two other forums it was pretty much confirmed that I was, indeed, an idiot for not realizing it sooner).

Again, thank you for your help, it is much appreciated.
I think I have no completed the assignment... finally!