# Thread: The First Problem You Solved?

1. ## The First Problem You Solved?

So, all through our lives we have been educated in various things. The general pattern of education in math has, in my experience, been "Problem, Principle, Walking Through the Steps of Proof, Description of Application, Homework."

But there's this thing that happens sometimes, to more or less of us: Sometimes you get the principle, and you solve it without being walked through the principle and the steps of proof. You just look at it, and work out the solution yourself from other things you know. I liken this to a proof of some other thing: being capable of original thought.

So, one of those things that I think has a lot to do with us, mathematics, and so on... What was the first mathematical concept for which the question was posed (or perhaps posed to yourself) and answered without being spoon-fed the way to find that answer?

2. Primary math ed from the reporting is changing, it is not important to get the right answer. Part of it is tied into kids who do poorly in math.

Looking back to grade school math for me was the introduction to problem solving, the trial and errr process, and logical thinking. How to structure a problem into manageable steps. Learning to concentrate.

In the media I listened to a supposed education expert say math is not a requirement for developing reasoning skills. Maybe so for areas like politics or social work.

Calculus is about dealing with rates of change. I think in terms of derivatives, related rates, and differentials even for non technical problems.

3. I can't think of anything particularly impressive, but recently I had to fit a curve to a series of data points for a pricing algorithm on a website.

I could see...
- what the curve was supposed to look like
- that the unit price decreased as quantity increased
- that the unit price could not go below a certain level
- that the unit price dropped quickly, then slowly, as quantity increased

I arrived at a solution by coming up with a function that solved each of the problems, one by one, then I combined them and re-factored it until it was neat. The solution is probably something that some people know off of the top of their heads, but it was a type of problem I hadn't actually had to solve until then. In high school we would have used a graphics calculator to give the curve of best fit, but in this case I needed to understand the various elements in the function so that I could adjust the starting price, the rate of change and the minimum price.

4. I remember the first time I was able to tie my own shoe.

5. I have no idea what the answer to this question is. I do remember in Algebra 2 (did awful in that class), I didn't get credit for solving a problem the "right" way. I have no memory what it was, but I remember that the answers were always proportional, so I followed the proportion and all was well and I got the right answers every time. Teacher did not like it, so I didn't get credit on the test. I didn't hate the teacher, but she wasn't a good educational fit for me.

I do like programming and in college, I developed a program to determine the "slimmest" gravity dam profile for a class project that required us to design a dam, in the global sense (not rebar level stuff). The math and procedures are cookbook, but how to get to the slimmest requires thinking. Granted, I just brute forced it by running an arbitrary number of random analyses. We weren't getting graded for making a program, so speed mattered in developing the code.

6. (1) My high school teacher thought I needed a challenge, so he assigned a classic. Given N points in general position on a circle, if you connect each pair then how many pieces is the circle's interior divided into? The solutions for small N are 1, 2, 4, 8, ?. I "invented" difference equations and found the 4th-degree polynomial solution.

(2) One or two years later I was asked to construct (or prove the existence of) an infinite sequence of A, B, C with no equal adjacent subsequences. A novel solution came to me in a flash while swinging on a swing.

To clarify the problem, if you start A.B.C.B.A.C.B.C.A.B.C.B.A.C.B you seem to be off to a good start.
You have equal subsequences A.B.C.B.A.C.B.C.A.B.C.B.A.C.B but they are NOT adjacent; there's a 'C' in between.

However, you've painted yourself into a corner:
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.A
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.B
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.C

But I was — and still am — an "idiot savant" :
Originally Posted by Wiploc
I remember the first time I was able to tie my own shoe.
I was last in my Kindergarten class to successfully tie my shoes.

7. Originally Posted by Swammerdami
(1) My high school teacher thought I needed a challenge, so he assigned a classic. Given N points in general position on a circle, if you connect each pair then how many pieces is the circle's interior divided into? The solutions for small N are 1, 2, 4, 8, ?. I "invented" difference equations and found the 4th-degree polynomial solution.

(2) One or two years later I was asked to construct (or prove the existence of) an infinite sequence of A, B, C with no equal adjacent subsequences. A novel solution came to me in a flash while swinging on a swing.

To clarify the problem, if you start A.B.C.B.A.C.B.C.A.B.C.B.A.C.B you seem to be off to a good start.
You have equal subsequences A.B.C.B.A.C.B.C.A.B.C.B.A.C.B but they are NOT adjacent; there's a 'C' in between.

However, you've painted yourself into a corner:
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.A
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.B
A.B.C.B.A.C.B.C.A.B.C.B.A.C.B.C

But I was — and still am — an "idiot savant" :
Originally Posted by Wiploc
I remember the first time I was able to tie my own shoe.
I was last in my Kindergarten class to successfully tie my shoes.
Same. Though today I'm the fastest person I know at thing shoes.

I can't take credit for that though; that all came from Ian's Shoelace Site.

8. Originally Posted by steve_bank
Primary math ed from the reporting is changing, it is not important to get the right answer. Part of it is tied into kids who do poorly in math.

Looking back to grade school math for me was the introduction to problem solving, the trial and errr process, and logical thinking. How to structure a problem into manageable steps. Learning to concentrate.
I agree. For me not only maths but all school curriculum is about developing of thinking not about getting the right answer.

9. Originally Posted by Jarhyn
So, all through our lives we have been educated in various things. The general pattern of education in math has, in my experience, been "Problem, Principle, Walking Through the Steps of Proof, Description of Application, Homework."

But there's this thing that happens sometimes, to more or less of us: Sometimes you get the principle, and you solve it without being walked through the principle and the steps of proof. You just look at it, and work out the solution yourself from other things you know. I liken this to a proof of some other thing: being capable of original thought.

So, one of those things that I think has a lot to do with us, mathematics, and so on... What was the first mathematical concept for which the question was posed (or perhaps posed to yourself) and answered without being spoon-fed the way to find that answer?
A good candidate for a first problem I posed myself because I actually had an application for the answer was working out a generic formula for the dimensions of an n-sided polygon such that its area matches that of a circle of a given radius, using trigonometry: Split the polygon into n triangles of two outer vertices and the centerpoint and calculate the triangles' area from the angle at the centerpoint (2 pi / n).

10. It is al a blur.
Circa 1980 I started in manufacturing. My first major project was setting up a statistical process control and reliability program at a medium sized company.

I used statistical methods to identify changes n field failure rates. When there was an inflection I'd start looking at field returns and always found a particular component that was a problem. Something oter than random failures.

In the pre pc days I ploted data by hand on probability paper for the Weibull distribution. Basic stuff but it was kew to me.

Statistics do work when properly applied. In manufacturing once I got rid of systemic problems the statistics stabilized. Any change in a mean and standard deviation n the process led to a problem somewhere.

In one case chips running through a plastic tube on an insertion machine was causing static damage to the chips.

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