Everyday problems requiring 'higher' math

[Turtle]

The argument is laid in another thread, that there is little or no day-to-day use for math above a certain level. For the purpose of this thread, 'higher' math means classes typically taught in 9th through 12th grades. This doesn't fit all school systems I relaize, but we gotta start somewhere.

 

The challenge here then, is to give real everyday problems you have encountered that either required higher math or that had more efficient/accurate solutions using higher math. This is not a quiz, so please show your work.

 

I would have posted a starting example, but I have to dust one off. :hihi:

 

Ready...set...GO! :hihi:

[Turtle]

A few months back I wanted to experiment with a solar trough oven, so I needed to lay out a large parabola as a pattern for cutting support frames.

 

Here is the finished article, a thread on the project, and my higher math solution. I think alternate methods of laying out a parabola qualify as higher math as well. :hihi:

 

I have settled on a size based on the available corrugated board on hand. Using a standard 'wardrobe' box, I cut 4 clean pieces 42" x +-18". From the large systems I looked at, the focus is nested below the level of the parabola's edges, but because I am using flammable paperboard I didn't want the tube too close.

Where p is the distance from the Focus to the Vertex of a parabola, I have settled on p=10". Then we have x^2=4py for the standard equation of an up pointing parabola. This gives me x^2=40y as the equation for my table of points to use in the layout.

This then gives me a 42 " trough 11" deep, leaving the tube 3/4 of the way inside the reflector.

http://hypography.com/forums/science-projects-homework/6465-solar-parabolic-trough-charcoal-oven.html?highlight=solar+trough

 

[Tormod]

I frankly can't think of any direct need for higher math that I've encountered lately.

[sanctus]

Well, for example wondering why you are pushed to the side when curving in a car...you need vectors to explain that.

 

Or things like if that thing has so much calories per so much grams how much calories do I get if I eat so much grams? Actually I have never done this, but I'm sure there are enough people on some kind of diet to who this happens quite often

[Turtle]

Well, for example wondering why you are pushed to the side when curving in a car...you need vectors to explain that.

 

Or things like if that thing has so much calories per so much grams how much calories do I get if I eat so much grams? Actually I have never done this, but I'm sure there are enough people on some kind of diet to who this happens quite often

 

I think we have to have more justification here than satisfying one's curiosity. We need real-world examples that counter the argument 'higher math is useless for everyday applications.'

 

With the calorie example: here again you yourself did not actually do it, so it doesn't meet our criteria.

 

Think of this as higher math on trial, and we need character witnesses to keep the prosecution from banishing higher math to elites. If we can't supply such examples, can we logically argue the need to teach higher math to any but a select few? ;) :cup: :hihi:

[freeztar]

By "Higher Math", I suppose you mean anything Algebra and above? (ie Geometry, Trig, Calc)

 

A month ago, I was doing some field work in TN. The tree planting plans that we had were vague, having no scale. The plans showed two rows of trees planted along a stream relocation adjacent to a road constructed about 7 years prior to our visit. They were spaced in a triangular, two-row alignment. The plans show the distance of the trees from the stream and from each other, so it was easy enough to answer my colleagues question about the offset, parallel tree spacing. I used Pythagorian logic to deduce the streamside row tree spacing which turned out to be about 17' and when we got to the site...

:hihi:

We counted three planted trees. A few recruits (mainly Salix nigra) were making a home, but the plantings either didn't happen or were obliterated early on.

 

I'll send a scan of my math-work when I get to the office on Monday. ;)

 

Unfortunately, higher math does not play into my job too much. Fortunately, my interests do! :cup:

[Jay-qu]

Finding volumes - while many people will say that there are simple formula's that can be remembered, these can all be derived from calculus, and of course there are those shapes that you could not work out without calculus.

[Turtle]

I frankly can't think of any direct need for higher math that I've encountered lately.

 

:eek: :cup: This doesn't bode well when the bailiff is first & fast to testify for the prosecution. :cup:

 

Finding volumes - while many people will say that there are simple formula's that can be remembered, these can all be derived from calculus, and of course there are those shapes that you could not work out without calculus.

 

I agree that is this the right kind or class of problems we are looking for, but unless you have a specific example of a real instance in your everyday life when you needed to make such a calculation and further knew how and did make it ,I don't think we can admit it as evidence.

 

This is the core of the problem you see. The prosecution charges we are holding a carrot on a stick and no one ever really eats it. An empty promise that if you learn this higher math someday you will use it. It isn't enough for us to simply suggest what use it could be, because that's the same old carrot. We need examples of what use higher math is. We need some beef!

 

Mmmmmm...this is well marbled...tasty freezy!

By "Higher Math", I suppose you mean anything Algebra and above? (ie Geometry, Trig, Calc)

 

Yes. I also think we ought to include Erasmus00's suggestion from the other thread, of 'discrete math' in the group.

 

...

I'll send a scan of my math-work when I get to the office on Monday.

 

Unfortunately, higher math does not play into my job too much. Fortunately, my interests do!

 

That's the ticket! We need another 50 like you. :cup: :eek:

 

:cup: :)

 

PS Perry Mason is in reruns again; love the court talk.:doh: :hyper:

[InfiniteNow]

Part of the issue, I believe, is how frequently we use higher math on an implicit and unconscious level. When we are driving and calculating our ability to transverse obstacles and deciding how long the approaching truck will take to reach us, or when crossing the street... that sort of thing.

 

When we plant a garden, we use our gut to place the plants into an order. We arrange the colors and the shapes and distances between them, not always with pencil and paper and formulae and algorithm, but definitely with math. The garden itself is a manifestation of geometry, a geometry imposed by our understanding of connections and order.

 

When we look at our baby's crib, checking the legs to ensure it's stable and not going to topple over when the lil'un is put to slumber we are using math. We make sure it's not wobbly across its various degrees of freedom. We support the weaker legs with braces or mechanical fasteners, knowing that this will make it more sturdy and rigid because we implicitly understand math.

 

Math is so ingrained into our psyche that it's most often expressed unconsciously. We find things beautiful, like vines climbing a trelice, or ripples in a pond, and we search for symmetries. When we play baseball and calculate when to swing the bat at the approaching ball, or which way to slide our glove to snatch the ball heading toward us.

 

We find a member of the opposite sex attractive because of the collective mathematical computation performed by all of our senses interpreting the stimuli this potential mate offers us. Their shape. Their color and reflective properties. Their scent. Their touch. We use math when intimate to maximize the pleasure for each participant, whether it be the angle of the hip or the softness of the caress.

 

Math gives us the ability to understand how neural cascades dictate the actions of our bodies and thoughts. Math gives us the ability to transfer electrical currents to millions of homes. Math gives us the ability to have plumbing in our homes and a roof over our head which will not fall in with the first gust of wind.

 

Math is just another way of appreciating the luminous beauty of the environment... the world... the universe. It provides a common language to all of the folks describing these things, and some people simply choose to explore the deeper histories and possibilities hidden within the language itself.

 

One can be a native English speaker, or Farsi, or French, or Mandarin, or Portuguese... and they can still share their pattern perceptions with others because of their shared implicit understanding of the language we call math.

 

Even if we do not specifically call each of these experiences by the title of math, that's what they are.

 

However, I was never really a fan of math myself. I always preferred science. :)

 

 

I apologize to Turtle for disregarding the request for specific personal examples. All I had to offer to today was some thoughtful prose on the topic. :eek:

[Turtle]

Part of the issue, I believe, is how frequently we use higher math on an implicit and unconscious level. When we are driving and calculating our ability to transverse obstacles and deciding how long the approaching truck will take to reach us, or when crossing the street... that sort of thing.

...

However, I was never really a fan of math myself. I always preferred science. ;)

 

 

I apologize to Turtle for disregarding the request for specific personal examples. All I had to offer to today was some thoughtful prose on the topic. :cup:

 

:doh: :hyper: Another ostensible supporter of the defendants tesifying for the prosecution. :eek: Your testimony has been duly recorded. :) I may have to put Drake on this one. :cup: :shrug:

[InfiniteNow]

:cup: :eek: Another ostensible supporter of the defendants tesifying for the prosecution. :doh: Your testimony has been duly recorded. :) I may have to put Drake on this one. :cup: :shrug:

 

Objection, your honor. My motivation and intent have been misconstrued, and I ask that the previous comments be stricken from the record. :hyper:

 

So noted. ;)

[Boerseun]

Well, in knifemaking, I sit with the problem of hollow-grinding the cutting edge of a blade after heat-treating it. The problem being, of course, that different blade shapes demand different curves. You can have ten different designs with steel thickness ranging from 2mm to 8mm, and the width of the hollow grind varies not only for aesthetical purposes, but for practicality as well. So what's the problem? I have only two grinding wheels! So how to solve it?

 

Firstly, me and my mate battled with the idea. Until we figured out that grinding at an angle to the same wheel will render different-sized grinds. In effect, one single wheel can create the any grind of your heart's desire, if you're willing to whack away at the calculator to determine the correct angle at which to attach the custom-made template to the wheelface. Seeing as every hollow grind is simply a section of a cylinder, the higher the angle, the broader and flatter the grind. Other knifemakers have vast collections of grinding wheels to get past this problem. I have now two wheels, and I can grind more accurate grinds over a range of specifications that they can't do! It's like having two spanners and being able to tighten every nut, metric and imperial, of any size!

 

Maths rock!

[Turtle]

Well, in knifemaking, I sit with the problem of hollow-grinding the cutting edge of a blade after heat-treating it. The problem being, of course, that different blade shapes demand different curves. You can have ten different designs with steel thickness ranging from 2mm to 8mm, and the width of the hollow grind varies not only for aesthetical purposes, but for practicality as well. So what's the problem? I have only two grinding wheels! So how to solve it?

 

Firstly, me and my mate battled with the idea. Until we figured out that grinding at an angle to the same wheel will render different-sized grinds. In effect, one single wheel can create the any grind of your heart's desire, if you're willing to whack away at the calculator to determine the correct angle at which to attach the custom-made template to the wheelface. Seeing as every hollow grind is simply a section of a cylinder, the higher the angle, the broader and flatter the grind. Other knifemakers have vast collections of grinding wheels to get past this problem. I have now two wheels, and I can grind more accurate grinds over a range of specifications that they can't do! It's like having two spanners and being able to tighten every nut, metric and imperial, of any size!

 

Maths rock!

 

:P Dude! You rock too! While I may never use this new insight, your hollow-grinding technique adds to something similar I used in woodworking. Using a table saw, I would clamp a fence at an angle to the blade rather than parallel, and by running boards over a partially raised blade I cut a cove. (Note: blade is raised in small increments for repeated passes of the board until reaching desired depth of cove). I never thought to angle the blade the way you describe, and now I see that doing so would give a much wider range of cove depth/width styles for a given blade. Muchas gracias!

 

So, this kind of problem is how I use higher math all the time. It just crops up, but as an opportunity to use what I already know. It is a valuable tool that does not really need the kind of justification the prosecution claims, anymore than the pocket knife needs justification in a pocket. You carry a knife because it often proves useful, and we ought to teach higher math on the same premise. :) :)

[max4236]

When I was designing my greenhouse I wanted to maximize the volume using a fixed supply of materials, to keep the costs down. So I used a bit of calculus to find the optimum dimensions.. It's kind of like that classic soup can problem. So far it been doing pretty good, just picked a bunch of fresh strawberries.