I have only 'scratched the surface' of this topic. You could start by looking at this article:

https://en.wikipedia.org/wiki/Key_(cryptography)

Bob

]]>You may not realise it, but every time you put in your on-line bank password, or send your credit card details, you are relying on prime number theory.

Ummm... Can you explain?

]]>I am afraid we have lost learn_everything forever. He never came back...

It was very disconcerting to hear someone saying the very words I said thousands of years ago. It is like that humanity has not changed in all that time. I wanted to change his mind.

On a more optimistic note, maybe he has absorbed huge amounts of mathematics... In that case I wish he would come back and help me.

]]>I work in the electricity industry, and because we work with things at an atomic level (which basically means that our cats and ladders are too small to see). So the only way for us to work things out is to do it theoretically - using maths (particularly square roots).

Hope that gives you a real world example of why square roots are important, because without them, you wouldn't have electricity.

]]>No need to thank me.

I have decided to just learn whatever mathematics I need

I think that is the most pragmatic decision you can make. I will try to provide a real world reason for the math you need.

]]>Here are some of my thoughts on this....

I think the three essentials you need in life are food, water, and shelter. Maybe a few more depending on who you are...

Everything else is not needed "to exist" or "absolutely essential""

Social studies, english, math, science, everything else, all the things you learn in school, you do not need to be alive.

Is it really "absolutely essential" to know a language? You could live in the middle of nowhere and sustain yourself without ever speaking a word. People will always be able to communicate, whether or not they understand each other, just so they can survive.

It all comes down to what decisions you want to make that will make you the person who you want to be...

Life is all about time. You are born and you die; it begins then it ends(as we know it). There is a set amount of time that you live your life. The more you know, the more you can do with your life. You make better decisions and get a better quality of life if you are a knowledgeable, quality person.

If you want to learn math and know how to solve things on a piece of paper before you spend all the time, money, and resources to do it in real life, then that is who you are...

If you want to be the person that spends 10-30 seconds measuring something with a floppy tape measure... that is who you are.

If someone who knows the Pythagorean Theorem can figure out the length of their roof by going into their attic, measuring the length of the floor and the height to the pitch, that is who they are.

If the other guy wants to just measure it the "old fashioned" way, bust out the scaffolding, and risk his life climbing onto the roof... that is who he is. (Though I wouldn't recommend this method right now where im at since theres about 5 inches of snow on the roof!)

What type of decision maker do you want to be? Do you want to be the guy in the attic or the one on the roof?

It seems like you are making a decision in your life right now that will define "who you are." If it is what you want, and you are to learn math in order to accomplish it, so be it!

I never knew that knowing what a coach purse was would have a positive impact on my life. But, low and behold, I saw a cutie and struck up a conversation over her coach purse. She was impressed I knew the brand.

You also never know when the math you learn will show up in your life. But, when it does, you will appreciate that part of your life a lot more... Once again... its just the type of person who you want to be.

All in all....

Having logical and mathematical knowledge is much bigger than a few real life examples, it is a way of being. It can be a part of you or not... it is your decision.

What's it in the end? Its the quality of life!

]]>It might look like that but she used A = 1 / 2 b * h, which is correct. Since b = h = L she ends up with:

She multiplies both sides by 2:

Take the square root of both sides.

The length L is 94.868 ft which she rounds to 95 ft. The zoo needs 2 of them so it is 190 ft. of fence needed.

learn_everything wrote:

It was only via the Pythagorean theorem that I was able to see how important square roots

That is not quite correct. In her problem she does not use the pythagorean theorem but the square root pops up just the same.

I did not want to confuse you before but here are some important formulas that use square roots:

]]>I didn't read the second link you posted because I perceived the first link to be incorrect. However I just read the second link you posted and I have to say, I think I get it now!! Thank you very much! (the building example w/ the bushes did it for me!)

But, in retrospect, square roots don't seem to be able to stand on their own in terms of being essential. It was only via the Pythagorean theorem that I was able to see how important square roots/Pythagorean theorem combination are. Anyhow, I guess that's irrelevant now though. I am glad to finally understand this though. I am excited to learn more!

P.S. - I think we should analyze that zoo example later though. I'm still blurry on that one.

]]>The only way now to get L algebraically, the Length of fence, is to take a square root of both sides.

The other page has 6 problems that all require a square root. And last I gave you one of mine that requires a square root.

(not impractical situations) in which I must use square roots or I will not be able to solve whatever it is I'm working on.

What is impractical about that? They were used to answer 7 different types of real world problems.

]]>

** Please keep in mind that I am not asking about "why do I need to learn math" in a general sense because simply stating that math is needed if you intend to study __ or __ doesn't help anyone. I am specifically asking for real world problems that I can attempt to solve on my own but ultimately I am able to eventually come to the conclusion that knowledge of the particular math concept is absolutely necessary to complete the real world task I intend to work on. **

I think your explanations are focusing almost exclusively on "why is math important" in a general sense while, as I stated, I am specifically looking for a real life practical situation that I can see myself in (not impractical situations) in which I must use square roots or I will not be able to solve whatever it is I'm working on.

However, I did like the zoo example you posted but what about:

http://www.ehow.com/how_5185561_calculate-area-isosceles-triangle.html

The formula she used is for a triangle, I thought an isosceles triangle had a different formula...

But anyway, I think that I should just deal with math when I am "forced to" in a practical sense. If I need it when I am building something in my daily life then it will be explicit and I won't have to wonder. The reason why I'll need will be right in front of me. Thank you nevertheless!

]]>learn_everything wrote:

Namely, is learning this concept of square roots essential or optional. I think optional. Is that correct?

That cannot be said. Lots of geometry, the roots of equations would just disappear. That is like saying let us leave out the number 17 because I am never going to use it. Nothing in math is really optional. The more you know the better off you are. How good would my german be if I left words out while learning?

learn_everything wrote:

I stated that square roots are not necessary and so did you.

Whoa, I never said that. Since the time of the ancient greeks mankind has known about square roots. Why would I recommend going back prior to that?

learn_everything wrote:

Honestly, I think we are on the same page really. The example about the nails that you listed shows this

Not yet. You did not understand the example fully. The guy who went and ran for the scale is the same as the guy who does not know what a square root is. He has to measure something that is apparent to everyone else who can add. What did you think of him?

learn_everything wrote:

In my opinion, IF square roots are absolutely essential, what I am asking should not be that difficult to answer.

That is a misconception. The simplest things are often the most difficult to explain. What do you mean by absolutely essential? They are absolutely essential for studying mathematics. Since math is being forced on you they are absolutely essential to you as well.

learn_everything wrote:

I am not able to accept something as vital if I am not able to see the vitalness of it.

This has nothing to do with math but it is the most compelling. You have the easiest decision in the world. You have no choice in the matter. That is how it is personally vital to you.

Obviously the fate of my cat did not mean very much. Take a look at some of these:

http://www.5min.com/Video/Learn-about-A … -286300938

All of these require a square root.

http://www.suite101.com/content/the-pyt … rem-a21010

To show you how tough a square root can be I recently worked on a tough one right here.

http://www.mathisfunforum.com/viewtopic.php?id=14832

My solution uses the pythagorean theorem 3 times. A square root is always necessary at the end of every pythagorean theorem.

]]>In my opinion, IF square roots are absolutely essential, what I am asking should not be that difficult to answer. I can't attempt to persuade a student or myself that this concept is important with what we've discussed so far.

Honestly, I think we are on the same page really. The example about the nails that you listed shows this. I stated that square roots are not necessary and so did you. They can help you and sometimes they can help you do what your doing a bit faster but they are not essential. And that is what I wanted to ascertain. Namely, is learning this concept of square roots essential or optional. I think optional. Is that correct?

]]>learn_everything wrote:

Square roots are not obligatory to learn since one actually could just measure the longest side with measuring equipment.

I think you are overestimating the ability to measure things. If I had a bucket with 10 lbs of nails in it and I added 6 more pounds of nails and then asked you how many pounds of nails are in the bucket. Would you go run and look for a scale? You would say 10 + 6 = 16 . There are 16 pounds of nails. The point is, why should I measure the distance when the square root gives it to me immediately?

Also square roots are just a tiny, tiny portion of math. Supposing I told you that the cat was stuck on the top of a 100 story building. And that you were 2 miles away. The square root is now the only way to get an accurate answer. Remember also that without the math the measuring devices we do have would not even exist.

Asking what good is math is something like asking what use is a child? It is often difficult to predict how some bit of knowledge will help you in the future.

Supposing I agree with you and say we do not need a square root. Why stop there? Let us assume we do not need to count. We do not need numbers. Did you know that humans were aware of set theory ( complicated math ideas ) before they even could count?

To sum up I can get the distance and the answer without any instrument. With just pencil and paper or maybe on a good day in my head. Wherever triangles, rectangles or squares exist, the square root is there.

I am not trying to explain everything by just a square root. You asked for an example and I showed one. That problem cannot be done without it. The more math we look at, the more you will see that without math we would not have a civilization. Our science and technology rest on it. Try to understand what I am saying.

learn_everything wrote:

Now, I am starting to study other fields that supposedly requires me to be very comfortable with very advanced mathematics.

Right here in the above quote seems to me to be the best reason to put aside your old philosophy that math was useless, in favor of one that says it is vital. You have a personal reason why math is important, do you not?

]]>So, is my thinking above correct about square roots? In summary, one uses square roots to determine the longest side of a triangle when one is building a structure or something else where the builder has two of the sides but not the longest side. Square roots are not obligatory to learn since one actually could just measure the longest side with measuring equipment.

Now, I wrote the first paragraph above but I don't know that I really believe it. Why? Because even if what I wrote above is correct I still don't see how a carpenter would use that information or would not be able to build a structure without that knowledge. When I was at work today, I specifically looked for things, structures, etc. around my workplace that a carpenter would have not been able to build without the knowledge of square roots. I didn't see a single thing. Perhaps you can list a 100% real life example where knowledge of square roots is an absolute must because I still don't get it. I am trying though.

]]>