Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

I am 24 yrs old and I am going through the entire curriculum on the mathisfun.org site as well as the p12.nysed.gov curriculum linked on the curriculum page. For now, I just want to ask why is there no real life practical application listed of each and every single concept listed on the curriculum progression pages?

I graduated high school but I was not good at math. That fact really didn't bother me because I saw no need for mathematics. I work as a translator so I did not see daily or at any time really any real life, real world problems that absolutely necessitated a ton of math that I was supposed to learn in school. Now, I am starting to study other fields that supposedly requires me to be very comfortable with very advanced mathematics. That is why I'm going through your entire curriculum (along with Khan Academy's curriculum) to solidify my knowledge of mathematics from the absolute basics to very advanced math.

BUT

I have to know very very precisely why I need to know each concept that is listed in the curriculums here and elsewhere. Not to belabor the point, what specific real world problem(s) specifically requires that the individual know the concepts listed on the curriculums. Now, of course, we all know that there are a lot of topics/concepts in the curriculum here, so what I wanted to do is perhaps have this thread as a place where I can list a concept and then someone can list the real world problem that can only be solved by proficiency of the aforementioned concept(s).

** 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. **

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi learn_everything;

Welcome to the forum. You have asked many difficult questions. Sometimes you have to learn a piece of math as a prerequisite to learning another piece which will be directly useful. Sometimes you just learn it for the same reasons that you might learn to play the violin or the electric guitar, why you would learn to paint or shoot pool. Because it is fun.

Post whatever you are learning each day and I will try to explain the utility of it. Also if you need help.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

Thank you, bobbym!

Well, so far, I am on the year one curriculum but while I am re-learning super basic concepts, I click on the other links on the page and I end up at more advanced concepts. So, if I am jumping around a bit and you feel that is hampering my understanding/progress then please just let me know and I will stick with curriculum until the concept that Im encountering makes sense.

So, I wonder what real world problem(s) absolutely requires the knowledge of:

#1. **square roots**

I have done some searching myself also and I have found this:

http://www.homeschoolmath.net/teaching/why_need_square_roots.php

This seems to be a good page for what Im asking about in general but I still didnt exactly understand the example that the author of that article mentioned regarding constructing a building. But I absolutely love the way he progressed with his example. Presenting a real world problem to students. Next, asking the students to solve the problem the best way that they know how. Finally, after the students are not able to solve the problem on their own (using the simple arithmetic that almost everyone can appreciate/accept), the teachers steps in and introduces to them the mathematical concept(s) that they are to learn at that time and shows them that they can only solve the specific real world problem with the math concept that he is teaching them.

This way the knowledge sticks and students can see how they can use it. I strongly feel that this would also encourage students to come up with other ways to solve the specific real world problem. This kind of student activity gets students involved with math and only makes the field of mathematics much better.

But anyway, the square root question above is my current question. Thank you!

*Last edited by learn_everything (2011-01-06 08:46:37)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi;

That page did an excellent job in explaining why you need square roots. You did say you did not quite understand their building example...

Perhaps the first time someone comes face to face with a square root is when he is learning about right triangles and Pythagoras.

Here is a little example of a problem that requires a square root.

See my cat up there, stuck on that pole? I have a ladder that is 21 feet long. I cannot get any closer than 17ft because the ground is too soft to support the ladder. I intend to use it as a ramp or plank ( the red line ) so he can just walk down. The question is, is my ladder long enough to rescue my cat? You need square roots to solve this and to know whether he is a goner or not.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

I still don't get it, bobby. I presume that what is going on in your mind with this is:

You have just found your cat in a tree. You don't have a ladder so you borrow your neighbor's. It is 21 feet long. You can measure the pole that the cat is in by standing the ladder up to the pole and marking where you think the pole stops and measuring that with a measuring instrument. So, you have two lengths. Ladder - 21 feet and pole - 13 feet. I don't know where you got 17 feet from and also I don't know what the ground being "too soft" means but I think what you are trying to do is set the ladder up in a way that if any pressure/weight is applied to it (the cat descending it), the weight will be evenly distributed. This is why you want to set the ladder up in a right triangle with the pole and the ground.

But I'm not sure what to do now though. I still don't understand why square roots are obligatory here. In a situation such as the example you listed, I would just position the ladder to where the cat could reach it and hold the ladder with assistance from others. Of course, I would attach a plank or something to the ladder first though because a cat can not just descend a ladder.

On a more general note though, perhaps one should learn math as they need it instead of learning it beforehand. If so, then my current approach is totally incorrect...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi learn_everything;

You are attaching too much reality to the problem. Remember it is just an example. The reason that is a right triangle is because poles are erected perpendicular to the ground. For the sake of the problem we say that the ground is too soft around the pole. Otherwise I would just put the ladder next to the pole and climb up the ladder. If I did that I would sink into the mud that is all around the ladder. The 17 feet is a given. We just happen to know that. We also say that the cat can come down the ladder. It can easily walk down the side supports of the ladder. They are only an inch and a half wide but cats are very dexterous and have narrow feet.

The point is we want to know whether the ladder or plank can reach the cat in the way I describe in the drawing. I did not expect you to know how to figure it, I was just showing you a problem that requires a square root.

To see the math working: We use Pythagoras who long ago stated that the squares of 2 sides of a triangle are equal to the square of the 3rd side ( longest side ). We call the third side the ladder, c.

By the theorem we have.

The boxed part is where the square root was used. We now know that the distance of the red line is 21.4 ft. Our ladder is 21 ft. It is too short, poofy is a memory unless we can come up with another idea.

In some problem like this but much drier is how I first saw a need for a square root. Any time we can set up a right triangle and they are all around us, we can find the third side of it by using a square root. That is the building example on the site you were looking at.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

hi learn_everything,

Having taught maths to children from age 11 to 18 for many years, I can understand why you, also, want to know "Why do I need this?"

I did try to show uses of a particular peice of mathematics, but sometimes it is hard to do this before the student has learnt enough to apply what has been learnt.

I also happen to think that the study of maths is good brain training; like doing sudoku or hard crosswords.

Also you can never be sure that an area of maths that seems to have no practical application, might one day become useful. A good example of this is in the number theory surrounding prime numbers. For years it just seemed to interest mathematicians and no one else. And then the internet was invented and now this theory is an essential part of internet security. 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.

There are also some mathematicians who think that it is good to study maths just because 'its there'. When my son completed his thesis in (S5, S5) amalgams and gained his PhD, I asked if I, as his supporting father and a taxpayer, could expect any practical use for all his work. With a great deal of pride and a cheeky grin he said "Certainly not!" and I agree with him!

In the summer of 1999 I achieved one personal ambition when I arranged a holiday in Fuschel, Austria to witness the total solar eclipse. The mathematics that enables astronomers to predict such events is complex and I think it involves square roots (plus a lot more). My reason for making the pilgrimage was to see the prediction in action. And thousands of others felt the same. It's very satisfying to have a 'model' for something in the real world, work out that that means X will happen, and then see it happen.

And here's another thing: Some of us think "Maths Is Fun"!

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

Bobbym, regarding square roots, my thought pattern was correct then, because you do, in fact, want equal pressure exerted on the ladder, so it doesn't dig into the "soft ground/mud". By the way, the examples you give me, PLEASE make them as real as possible. If not then I will not be able to understand it.

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.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi learn_everything;

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?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

I think you are missing my point. I am not able to accept something as vital if I am not able to see the vitalness of it. I can not state that math is important "just because it is". There are some areas of math that I know are essential and are used everyday. I did not inquire about them, I am inquiring about square roots since I don't see what makes them essential to learn. If you were to tell me that one doesn't really need to know square roots and that learning it is optional then I would be at ease, I would notate that in my notes, and I would happily move along and search for other concepts that don't make sense to me. But since you feel they are absolutely necessary to know then I really would like to know why.

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?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi;

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 mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

** 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!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

No, you missed the whole thing. That triangle problem requires a square root right at the end. She did not use an arbitrary formula just so she could get a square root. It was unavoidable. In that problem you have to end up with:

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

Oh no, I was agreeing with you regarding the zoo example. It's just the fact that she seemingly used the wrong formula confused me and sort of invalidated the rest of what she did in the problem. (at least in my mind)

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.

*Last edited by learn_everything (2011-01-07 21:13:37)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi;

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:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**4DLiVing****Member**- Registered: 2011-01-08
- Posts: 22

Hi Learn Everything;

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!

Offline

**learn_everything****Member**- Registered: 2011-01-05
- Posts: 9

I am still here bobbym. I have decided to just learn whatever mathematics I need when/if the situation calls for it in my upcoming job endeavors. So, I will post any job-related math problems I have here in the future if that is ok with you. Thank you!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi learn_everything;

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**mogduck****Guest**

I just came across this thread by accident, but i think i can give a good example (without going into too much detail).

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,704

Hi;

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

Pages: **1**