Math in Everyday Life

Date: 09/22/2000 at 07:56:20
From: Jay Flores
Subject: Relation of math to everyday life

Peace be with you, Dr. Mathematics,

I'm just an ordinary student from a regional science high school. 
Could you please tell me about the relations of mathematics to your 
everyday life for one day, specifically relations involving geometry, 
algebra, and trigonometry? How would math be related to your everyday 
life if you were a student?

As I have started my story, it is very simple. When I woke up I saw 
the clock and figured out that it was a circle... and that's it. 
Circles are part of math, but I want the story to be related to 
geometry or trig, which is a little bit difficult. Thank you for your 
concerns.

Jay Flores
Philippines

Date: 09/22/2000 at 16:10:17
From: Doctor Ian
Subject: Re: Relation of math to everyday life

Hi Jay,

Here's one interesting use of geometry. Suppose you want to leave 
holes in the street, so men can get underneath to fix pipes and 
electrical cables.

When the holes aren't being used, you want to cover them with 
something very strong, like a heavy metal lid, so cars can drive down 
the street without being damaged.

Of course, if a man is down in the hole, and such a heavy cover falls 
on him, he's going to get hurt pretty badly. So it would be nice if 
the lids would fit _on_ the holes, without being able to fit _through_ 
the holes. It turns out that there is only one possible shape that 
will work. Can you guess what it is? (If not, take a look at a manhole 
cover.) Can you see why other shapes won't work?

Here is another way that you might use math in your everyday life. 
Suppose you live in a room that is 8 feet from floor to ceiling, and 
you want to build a bookshelf on the floor and then raise it to lean 
against the wall.

You can't make it 8 feet tall, because at some point while you're 
raising it, it's going to be in a position like this:

               .
             .   .
           .   .
         .   .
       .   .
     .   .
       .

That is, in order to stand it on end, it has to be able to clear the 
ceiling with one corner while standing on the other. You would have to 
use the Pythagorean theorem to answer this question: What's the 
tallest shelf you can build this way?

It isn't something you do every day, but if you wanted to estimate the 
height of a building on campus, you could pace some distance away from 
it, measure the angle that it subtends from that distance, and use 
trigonometry to compute the approximate height.

The truth is, there aren't a lot of everyday uses for geometry and 
algebra and trigonometry, which is why most adults who have been out 
of school for 10 years can't remember anything about them. They're 
worth learning because they're fun, and they're worth learning if you 
want to have a career that involves designing or creating or building 
new things.

They're also worth learning because knowing them can make it harder 
for people to lie to you. Here's an example. Let's say that I want you 
to think that something is a much bigger problem than it is, so that 
you'll elect me to office or agree to hire me on the basis of my 
promises to "handle" it. If the thing has doubled since 1960, then I 
can draw a graph like this,

     Mosquito Bites

                +-----+300
                |     |
                |     |
     +--+150    |     |
     |  |       |     |
     |  |       |     |
     +--+       +-----+
     1960        2000

which uses icons (a small mosquito and a large one). The one on the 
right is twice as tall, but it's also twice as wide - so although the 
numbers are telling you that the increase is 100%, the picture is 
telling you that the increase is 300%. If you're not paying attention, 
you'll walk away with the impression that the danger of mosquito bites 
is greater than it is.

And of course, since I'm putting together the graph, I probably won't 
mention that the change in population means that the number of 
mosquito bites PER PERSON hasn't really changed, and may even have 
gone down.

Basically, people who are comfortable with math will always be able to 
use it to trick people who aren't comfortable with math into giving up 
their money and freedom.

I hope this helps. Write back if you have more questions, about this 
or anything else.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/06/2000 at 09:19:25
From: Jay Flores
Subject: Re: Relation of math to everyday life

Dr. Math,

Hello there, I greatly appreciate your help. I know that thanking you 
is not enough but that's all I can say with an open heart. I believe 
people like you should be so blessed. Bless your heart.

Well, I almost got that but sad to say I'm grasping with math. Would 
you please tell me some of the calculations in it? I would greatly 
appreciate it if you would translate it to a story, you know, like one 
day I want to make a cabinet but... so I used the what formula... and 
then the calculations...

I just want to thank you in advance. I believe in you and thank you.

God Bless,
Jay Flores

Date: 10/06/2000 at 18:34:51
From: Doctor Ian
Subject: Re: Relation of math to everyday life

Hi Jay,

I don't know if you'll believe this, but I just spent about an hour 
writing a story for you, and when I tried to submit it, my browser 
crashed, and it was lost.

It was a really good story, too! So I'm upset about it, but I think 
maybe this means that I wasn't supposed to do your homework assignment 
for you.

I can tell you about some equations you'd use in your story, though.

If you wanted to set your alarm clock for 8 hours past 10 o'clock at 
night, you'd use modular arithmetic:

     (10 + 8) modulo 12 = 6

That is, you'd set it for 6 o'clock in the morning.

The height of the shelf would depend on how deep it was. For example, 
if it were one foot deep, then you would use the Pythagorean theorem:

     diagonal^2 = height^2 + depth^2
         height = square root( diagonal^2 - depth^2)

where 

     diagonal = 8 feet
     depth    = 1 foot

If you found yourself wondering about manhole covers, the reason that 
you can't drop one into a hole is that for any shape _but_ a circle, 
you can turn the shape sideways and fit it through itself:

       ------          |
      /      \_____    |  Projection in this direction ->
     /____________/    |

     --------------
   
      Projection in this direction |
                                   V

This is because every projection of a circle from two dimensions to 
one has the same size.

If you wanted to buy stamps for a letter, you could divide the price 
of a stamp into the amount of money you want to spend, to get the 
number of stamps you can buy.

And when you're cooking dinner, if the recipe is for 4 or 8 people, 
you can divide all the amounts by 4 or 8 to figure out how to make 
enough for just one person.

I'm sorry you're not going to get that story. But I don't think I 
could write it again.

I hope this is helpful anyway. Write back if you have more questions, 
about this or anything else.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/11/2000 at 05:57:26
From: Jay Flores
Subject: Re: Relation of math to everyday life

Hello Dr. Ian,

It would really be great if you could do just one page of the story, 
or at least 5-6 situations using math equations of my year. I really 
thank you for your kindness and the perseverance that you're showing. 
It is not just for me but also for the benefit of all, so they will 
not ask you the same questions. If you have some illustrations, could 
you please show them to me? I can't understand your story. Thanks for 
everything and blessings be with you.

Care,
Jay

Date: 10/11/2000 at 16:33:44
From: Doctor Ian
Subject: Re: Relation of math to everyday life

Hi Jay, 

Here's how a story might go. It's 10 p.m. and you're about to go bed. 
You need to sleep for 8 hours, so you have to figure out when to set 
your alarm clock:

     10:00 + 8:00 = 18:00 
                  = 12:00 + 6:00

so you have to set it for 6:00 a.m.  

When it goes off, you wake up, and you want to make some pancakes. But 
your recipe book only has a recipe for 6 people. You're hungry enough 
to eat enough for two people, so you divide everything in the recipe 
by 3.

You go to the store to buy some wood to build shelves, for a room 8 
feet high. That means the diagonal can't be more than 8 feet. So you 
use the Pythagorean theorem to figure out the length of the boards:

     diagonal^2 = height^2 + depth^2  
     height = square root( diagonal^2 - depth^2)

You know that 
  
     diagonal = 8 feet
     depth    = 1 foot

so you plug those numbers into the formula, and get the right length. 

On the way home from the store, you stop to buy some stamps at the 
post office. Each stamp costs 32 cents, and they come in books of 10 
and books of 50. You have $10, so you figure you can buy three books 
of 10 and have some money left over.

On the way home from the post office, you notice that some 
construction guys have a manhole open, and you wonder why you never 
hear about anyone being killed by a manhole cover dropped down a 
manhole. You take out a coin and look at it from the side, and you 
notice that no matter which way you turn it, it has the same width. 
And you realize that no other shape has this property. Which must be 
why they make manhole covers round, instead of square, or triangular, 
or any other shape.

You get into bed without setting the alarm, and start counting sheep 
to try to fall asleep. It's not working, but you notice that in your 
mind, a sheep jumps over a fence every two seconds, and you wonder how 
many sheep you'll have to count if you stay awake for an hour. You 
figure, an hour is 60 minutes, and a minute is 60 seconds, so that's 
3600 seconds, so at one sheep every two seconds, you'll count to 1800 
if you're still awake then. And you get so tired from doing those 
calculations that you fall asleep right after you come up with the 
answer.

I hope this helps.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   

Date: 10/12/2000 at 05:54:27
From: Jay Flores
Subject: Thanks for all your help! it's the best!

Dr. Ian,

I personally thank you for helping me out with that. It actually 
helped me in understanding math as a medium for communication. I 
believe that this service is one of the best services in the world and 
that's a very undeniable fact! The story that you gave me doesn't help 
me just for my own advantage but for all people's advantage as well.

Dr. Ian, many thanks, I greatly appreciate it. You're not just 
helping, you're actually teaching!

Care,
Jay Flores of the Philippines