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 about four 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...

3. Who is "Joe" in Erdos' special jargon? Who are the "bosses" and the "slaves?"
Again, not sure where to go with this. I really can't find much information regarding "Erdos' special jargon" or any information on what the "bosses" and "slaves" might be. Perhaps I'm just not looking in the right place...

4. 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 lastly, would anyone be willing to check a few of my answers for some of the other questions? I'm not entirely sure if I got the correct answers for these ones, or if they make sense...

1. What is Sperner's Lemma used for?
It can be used for effective computation of fixed points. It can also be used in root-finding algorithms and fair division algorithms.

2. Who is credited for making the first logarithm table? How about the first common log table?
Napier was the first to make a logarithm table. Henry Briggs published the first common log table.

3. What equation did Euler want inscribed on his gravestone?
e^pi*i=0, “Euler’s identity”

4. What is the Lorenz Butterfly Attractor, and what does it have to do with the Butterfly Effect?
Named after Edward N. Lorenz, it is a fractal structure corresponding to the long-term behavior of the Lorenz oscillator, which is a three-dimensional dynamical system that exhibits chaotic flow. The map shows how the state of a dynamical system evolves over a period of time in a complex, non-repeating system.

5. What does the Rössler attractor look like? What makes it “strange”?
In appearance the attractor looks like a flat circle, with some three-dimensional lines (some rounded and coming back into the main portion, some jutting off into space) with different points.
Note: I'm not sure what to say about what makes it "strange"...

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

 

[Deleted member 4993]

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 about four 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...

3. Who is "Joe" in Erdos' special jargon? Who are the "bosses" and the "slaves?"
Again, not sure where to go with this. I really can't find much information regarding "Erdos' special jargon" or any information on what the "bosses" and "slaves" might be. Perhaps I'm just not looking in the right place...
I don't know what type of search you did do - about Paul Erdos. But Wiki states:

Other idiosyncratic elements of Erd?s' vocabulary include:

* children were referred to as "epsilons" (because in mathematics, particularly calculus, an arbitrarily small positive quantity is commonly denoted by that Greek letter (?));
* women were "bosses";
* men were "slaves";
* people who stopped doing math had "died";
* people who physically died had "left";
* alcoholic drinks were "poison";
* music was "noise";
* people who had married were "captured";
* people who had divorced were "liberated";
* to give a mathematical lecture was "to preach" and
* to give an oral exam to a student was "to torture" him/her.


4. Suppose that a planar graph has 97 vertices and 132 faces. How many edges must it have? <<< Euler's formula V - E + F = 1
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 lastly, would anyone be willing to check a few of my answers for some of the other questions? I'm not entirely sure if I got the correct answers for these ones, or if they make sense...

1. What is Sperner's Lemma used for?
It can be used for effective computation of fixed points. It can also be used in root-finding algorithms and fair division algorithms.

2. Who is credited for making the first logarithm table? How about the first common log table?
Napier was the first to make a logarithm table. Henry Briggs published the first common log table.

3. What equation did Euler want inscribed on his gravestone?
e^pi*i=0, “Euler’s identity” <<< That's incorrect. The identity is: e[sup:2i1onden]i*pi[/sup:2i1onden] + 1 = 0

4. What is the Lorenz Butterfly Attractor, and what does it have to do with the Butterfly Effect?
Named after Edward N. Lorenz, it is a fractal structure corresponding to the long-term behavior of the Lorenz oscillator, which is a three-dimensional dynamical system that exhibits chaotic flow. The map shows how the state of a dynamical system evolves over a period of time in a complex, non-repeating system.

5. What does the Rössler attractor look like? What makes it “strange”?
In appearance the attractor looks like a flat circle, with some three-dimensional lines (some rounded and coming back into the main portion, some jutting off into space) with different points.
Note: I'm not sure what to say about what makes it "strange"...

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

 

[Blue Leader]

Ah, thank you. Though I have one question about Euler's formula...
V - E + F = 2

I understand that the V would be 97 and the F would be 132... But what do I do with the E?
97-E+132=2...

 

[Deleted member 4993]

Ah, thank you. Though I have one question about Euler's formula...
V - E + F = 2

I understand that the V would be 97 and the F would be 132... But what do I do with the E?
97-E+132=2...

Did you read your "own" post carefully? What was your original question?

There is a correction for that formula:

for planar graph: V + F - E = 1

 

[Denis]

Ah, thank you. Though I have one question about Euler's formula...
V - E + F = 2
I understand that the V would be 97 and the F would be 132... But what do I do with the E?
97-E+132=2...

E = 97 + 132 - 2
E = 227
Are you saying you were unable to solve for E?
If so...well, no comments.

 

[Blue Leader]

Ah, thank you. Though I have one question about Euler's formula...
V - E + F = 2
I understand that the V would be 97 and the F would be 132... But what do I do with the E?
97-E+132=2...

E = 97 + 132 - 2
E = 227
Are you saying you were unable to solve for E?
If so...well, no comments.

No need to get like that. I realized this morning what I needed to do, I guess last night I just wasn't thinking clearly. I forgot that it needed to equal to 2 so I needed to find a number that, once the equation was "finished", everything would equal to 2 at the end.
I simply forgot or wasn't thinking clearly, that's all. Surely I'm not the first person to do that.

 

[galactus]

Here is 200 digits of e:

2.71828182845904523536028747135266249775724709369995957496696762772407\
6630353547594571382178525166427427466391932003059921817413596629043572\
9003342952605956307381323286279434907632338298807531952510190

Thanks to Mathematica


In general, the Cantor set consists of \(\displaystyle 2^{n}\) subsets, each with magnification factor \(\displaystyle 3^{n}\). So the fractal dimenstion is

\(\displaystyle \frac{log(2^{n})}{log(3^{n})}=\frac{nlog(2)}{nlog(3)}=\frac{log(2)}{log(3)}\approx .630929753571\)

 

[Deleted member 4993]

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 about four 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. <<< Really!!

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...

From Google by way of Wiki

e = 2.71828182845904523536….