Hello again,

I forgot to mention that the 'reverse' formula here is actually referred to as the "inverse" function.
There is a bunch written on calculating inverse functions for more complicated functions but the main idea goes like this.
If you have a function like:
y=x^2

then you want to solve for x rather than y.
For this function it happens to be easy but there are two possibilities:
x=sqrt(y)
x=-sqrt(y)

Some other functions are more difficult such as:
y=x^4+x^3+x^2+x+1

so you'd have to read up on how to handle the more complicated ones.
Sometimes only a numerical solution is possible.

The original question as posed was simply a first degree polynomial (aka a linear function). Easy enough using the techniques described but for higher degrees the TS would need a more involved polynomial root-finding algorithm. (Given that every Nth-degree polynomial contains exactly N roots on the complex plane).

 

Maths was never my strongest subject and sometimes I struggled really hard to understand some simple problems whilst at the same time I could easily grasp some more complicated ones with seemingly an intuitve skill which I have no idea how I aquired it. I well remember once working on a project with some colleagues who were having difficulty solving a problem, when suddenly, without really studying their work at that point, I could "see" the solution. It was almost as though a video of the process was being played in my minds eye and I had to quickly write it down before I forgot it. I then spent several hours with my collegues working through it only to find it was correct!!
I have had similar experience several times in my life, two of note were when I had a small milling machine that used an induction motor to power it. Speed change was by moving a drive belt on stepped pulleys. The lowest speed was too high for machining some iron castings and I spent some time wondering how to slow it down.
Some weeks later, I was driving to my workshop, and as before, a video played in my head of every last detail of how to incorporate an epicyclic gearbox inside the motor pulley. As soon as I got to my work I grabbed a jotter and sketched it out. It was so sucessful that I had a local engineering company make them and we marketed them as "The R.M.C back gear pulley" and many dozens were sold until a very large manufacturer purchased the licence rights from me. I still have the original prototype I made on my little Myford super seven lathe.
The second of note is that I have written a great deal of poetry, and on many occassions I have to stop whatever I am doing, quickly get pen and paper and write like mad, THEN I read what I have written and wonder where on earth it came from!!!
Maybe I'm just weird, but I do know of another person with the same Gift, or should that be affliction?
Getting back to the t,s remarks about not being strong at maths, I would say this:- Study as much as you can, but NEVER be afraid to ask for help from others. I have a friend whose Life and hobby is the study of pure marhs, I have on many times received help from him and there is no point in being too proud, or fearful of looking stupid for asking for help.

 

Maths was never my strongest subject and sometimes I struggled really hard to understand some simple problems whilst at the same time I could easily grasp some more complicated ones with seemingly an intuitve skill which I have no idea how I aquired it. I well remember once working on a project with some colleagues who were having a difficulty solving a problem, when suddenly, without really studying their work at that point, I could "see" the solution. It was almost as though a video of the process was being played in my minds eye and I had to quickly write it down before I forgot it. I then spent several hours with my collegues working through it only to find it was correct!!
I have had similar experience several times in my life, two of note were when I had a small milling machine that used an induction motor to power it. Speed change was by moving a drive belt on a stepped pulleys. The lowest speed was too high for machining some iron castings and I spent some time wondering how to slow it down.
Some weeks later, I was driving to my workshop, and as before, a video played in my head of every last detail of how to incorporate an epicyclic gearbox inside the motor pulley. As soon as I got to my work I grabbed a jotter and sketched it out. It was so sucessful that I had a local engineering company make them and we marketed them as "The R.M.C back gear pulley" and many dozens were sold until a very large manufacturer purchased the licence rights from me. I still have the original prototype I made on my little Myford super seven lathe.
The second of note is that I have written a great deal of poetry, and on many occassions I have to stop whatever I am doing, quickly get pen and paper and write like mad, THEN I read what I have written and wonder where on earth it came from!!!
Maybe I'm just weird, but I do know of another person with the same Gift, or should that be affliction?
Getting back to the t,s remarks about not being strong at maths, I would say this:- Study as much as you can, but NEVER be afraid to ask for help from others. I have a friend whose Life and hobby is the study of pure marhs, I have on many times received help from him and there is no point in being too proud, or fearful of looking stupid for asking for help.

I have that gift as well. I was an applied math major in college. This one professor gave group exams, where we’d have to create a particularly difficult proof. I would “see” the answer with all of its intermediate steps. My team mates would provide the specific rules and proofs we had studied. A task our classmates would struggle on for days, collectively we’d have done in a few hours. And spent the rest of the time downing cold beers.

 

Hi,

I did really good in math after i got a great teacher who knew how to motivate kids.
But you reminded me my favorite subject was cold beers. In fact, I am still studying that subject intently

 

Maths was never my strongest subject and sometimes I struggled really hard to understand some simple problems whilst at the same time I could easily grasp some more complicated ones with seemingly an intuitve skill which I have no idea how I aquired it. I well remember once working on a project with some colleagues who were having a difficulty solving a problem, when suddenly, without really studying their work at that point, I could "see" the solution. It was almost as though a video of the process was being played in my minds eye and I had to quickly write it down before I forgot it. I then spent several hours with my collegues working through it only to find it was correct!!
I have had similar experience several times in my life, two of note were when I had a small milling machine that used an induction motor to power it. Speed change was by moving a drive belt on a stepped pulleys. The lowest speed was too high for machining some iron castings and I spent some time wondering how to slow it down.
Some weeks later, I was driving to my workshop, and as before, a video played in my head of every last detail of how to incorporate an epicyclic gearbox inside the motor pulley. As soon as I got to my work I grabbed a jotter and sketched it out. It was so sucessful that I had a local engineering company make them and we marketed them as "The R.M.C back gear pulley" and many dozens were sold until a very large manufacturer purchased the licence rights from me. I still have the original prototype I made on my little Myford super seven lathe.
The second of note is that I have written a great deal of poetry, and on many occassions I have to stop whatever I am doing, quickly get pen and paper and write like mad, THEN I read what I have written and wonder where on earth it came from!!!
Maybe I'm just weird, but I do know of another person with the same Gift, or should that be affliction?
Getting back to the t,s remarks about not being strong at maths, I would say this:- Study as much as you can, but NEVER be afraid to ask for help from others. I have a friend whose Life and hobby is the study of pure marhs, I have on many times received help from him and there is no point in being too proud, or fearful of looking stupid for asking for help.

I would consider myself to be more the intuitive type as well. For example, speaking of polynomials, an unusual idea came to me for solving them using Lucas-like sequences. Seemed a bit implausible but went ahead and wrote some code to test the hypothesis out anyway. I was actually very surprised when it started spitting out polynomial roots. It just came to me from out of the blue! I'd much rather be the rigorous-knowlegable type though honestly (like WBahn!) but like you say it is something of a gift in it's own right.

 

My strength was in geometry class.
We would have a race to see who would be the first to solve the problem and be the first to scribble Q.E.D. on their solution sheet.

 

Hi,

When i first learned calculus i was amazed at how we could study quantities that change and the effects from that. Before that it was mostly static variables.

But i have to study tonight there might be a test tomorrow on how many chugs does it take to down a 12 ounce bottle of Heineken, and i dont want to fail that one it's for extra credit