# Thread: Math History Questions (MTH105)

1. ## Math History Questions (MTH105)

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 is a math problem that I need to solve? An equation?

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.

2. This is not a homework service
So what exactly do you expect from us?
We are not going to do this work for you!

3. I'm not asking you to do the work for me, I just need to know where to go with it. I'm just asking for some clues on how to finish the questions I had, I'm not asking it to be done for me.
Like how would I calculate the digit in the thirtieth decimal place of the decimal expansion of the number e that is the base of the natural logarithms?

But if help can't be given than that's alright, I'll just keep looking around and hopefully I'll run across something that can help me.
Thanks anyway.

4. Look into Howard Eves' AN INTRODUCTION TO THE HISTORY OF MATHEMATICS. You can do your own search.

5. $\displaystyle e^x = \sum_{n = 0}^\infty{\frac{x^n}{n!}} = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots$.

Let $\displaystyle x = 1$ and evaluate to your desired accuracy.

6. Question 1. Here's e for you. I don't know how hard you searched the web - this took me about 30 seconds to find with Google:

http://www.mu.org/~doug/exp/100000.html

As for question 3 - another 15 seconds on Googel led me to this:
http://en.wikipedia.org/wiki/Planar_graph

Note Euler's formula about half way down the page.