It is not a weird question. It is the beauty and pleasure of finding things out.

"We must know. We will now." David Hilbert.

Its mostly natural curiosity. To know what the answer is or how it is done or why it is done that way. To know more than you did before the multiple losses and the "victory". The losses bring you to victory. They father it.

For some, if not all at some point in their lives or even always, its the victory also of winning one more time. Its the confirmation you are good enough and better than before and still unstoppable. It is a superficial reason but very natural also.

To be fair if the problem is very interesting and solves some mystery of the world rather than just another difficult or creative problem in general, if it has some substantial application that changes something around us, the joy experienced with the solution or even synthesis is way bigger than any other form of pleasure experienced by humans comparable not with the ephemeral satisfaction of sex or food or water consumption in thirst but maybe the experience of love towards someone very precious or the experience of their love.

And yet if the solution is important one knows it is even above individual love. Because it is love for mankind and wisdom addressed to all. It is the ultimate gift of complexity. And all prior little frustrations and wins all your life in little unimportant or even cute but limited range problems are just training for that moment that may never come but should if you care for clarity and the truth about logic and natural law. You will be rewarded if you care. To finally know what you or nobody ever did before is the ultimate vindication for existing. The purpose of complexity is to build wisdom and explore natural law yielding higher complexity.


You face tilt and frustration and curse the hell out of the world sometimes but you do not really mean it. If you are experienced and wiser you actually care more for learning from failure and noticing what it tells you. Sometimes reverse engineering a failure gets you the answer. See experience as a gift always. Then failure is actually a process of experience building that takes you closer to the answer and may for this reason be very important. The more past victories you had of course on tough problems the higher the confidence and courage acquired. You can endure more, you have patience. You know what will happen in the end. So not being able to solve something is now a challenge, a confrontation you must have that is intriguing and will only lead to victory or learning something new. So why not engage?

What you are effectively chasing though even above all difficult problems is this moment of clarity and higher awareness often found in the simplest of realizations.

"I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: " If a person falls freely he will not feel his own weight." I was startled. This simple thought made a deep impression on me. It impelled me towards a theory of gravitation." Albert Einstein

If you get this then no amount of hard work following and technical failures will even frustrate you enough to not lead to the answer (ie field equations years later). The answer is synthesis of course. And likely it is what will drive the next beautiful thoughts in others decades or centuries later.


See all your frustrations as training for the real battle ahead. Train well. Clarity will be the reward.

lol

Interesting and ty


name of documentary?

simplest form of 26 over 39 = 2/3

Just curious if someone can explain what would the term used to do this backwards? for example 2/3 to 26/39

Also 0.6666666666666667 to 2/3?

with the first 26/39 they call it greatest common divisor of 26 and 39.

So just wondering is there a term used similar to to greatest common divisor but instead for 2/3 to 26/39 and 0.6666666666666667 to 2/3?

thanks just watched it cool guy

The greatest common divisor doesn't quite mean what you think it means, though I can see why you're using it the way you are.

A divisor (d) of a number (n) is some number such that d divides n evenly. (Alternatively, there exists an integer k such that d*k = n.)

A common divisor of two numbers a and b is a number that is a divisor of both a and b.

The word "greatest" can be interpreted as "biggest."

So the greatest common divisor of two numbers is the biggest number that divides both of them.

This doesn't get turned around nicely because there is no "greatest" number going in the other direction.

2/3 = 4/6 = 6/9 = 9/12 = ...

The phrasing we use here is that we're finding an "equivalent" expression for the original. So 2/3 is equivalent to 26/39. We might also say that we are "rewriting" the fraction with a specific denominator. The process could be described by saying that we are multiplying the numerator and denominator by the same value.

But to my knowledge, there's no standardized term for this.

Thanks or explaining.

for*

Do any of you recommend sites like Wolfram Alpha or MathPapa, or similar sites? - these are calculators (apparently ideal for those that struggle in math ) they also explain how to do the maths step-by-step.

You can multiply anything by 1 without changing its value. So in this case, we can multiply 2/3 * 13/13 to get 26/39, with 13/13 being another way to represent 1.

To go from 0.6666666666... to 2/3

set x = 0.666666666...

Multiply both sides by 10

10x = 6.66666666....

Subtract the second equation from the first. This works because both sides of the equation are equal, and subtracting the same thing from both sides of of an equation preserves the equality.

10x = 6.6666666666...
- x = - 0.66666666666...
---------------------------
9x = 6

x = 6/9

x = 2/3

It's a little more complicated when the repeating decimal is more than one place, or is preceded by a non repeating part, but the same strategy can be used:

http://www.basic-mathematics.com/con...fractions.html

thanks

Any number that permanently repeats post decimal point digits of a cycle n say can be represented (to reveal its rational nature) as a sum of a part up to the beginning of the repeat plus a ratio of the cycle digits sequence over the same number of 9s times 10^-x where power x is the number of places after the decimal point beyond which the repeat begins.

Example;

13.556345678345678345678....= 13.556+10^-3*345678/999999 (Of course 13.556=13566/1000)

This of course can then be further worked out to produce a ratio of 2 integers establishing its rational character.


You can prove that later when you know more with infinite geometric series properties.

I use Khan Academy with my daughter, so here's what I'd recommend:

If you understand a concept, there's no need to drill on it. Focus on things that give you trouble and just keep pushing forward. Do the mastery challenges without referring to any notes or videos.

Focus on the PROCESSES. Don't use shortcuts because you need to understand the proper processes as things get more complex.

Example:

If you see 3x=15, don't just say "x=5" and move on. Go through the problem step by step on paper.

If you keep taking the mastery challenges you'll earn mastery in those boring areas that you understand without drilling. But periodically check back to see if there are any gaps.

Good luck.

I believe Khan Academy refers to these as "equivalent fractions" and "equivalent ratios."

2/3 and 4/6 are equivalent fractions, but the algebraic mechanism of doing the following to create equivalent fractions is without a standardized name.

2/3 = (2*2)/(3*2)

(Equivalent fractions = noun, the process of getting them = verb)

I move that it be called "complification".

I also think there should be a name for parallelograms that are not rhombuses.

nondegenerate parallelograms

No.

https://en.wikipedia.org/wiki/Degeneracy_(mathematics)

Why no?

"In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class. Degeneracy is the condition of being a degenerate case."

This is exactly what is going on here. A measure zero set vs the set of parallelograms is the one that all sides are equal. It is a simpler class. The limit is one side becoming equal to the other.

Exactly, huh. Aside from that your use of "measure zero", "simpler" and "limit" (of what?) are undefined.

You could make a similar case for those parallelograms having one side twice the length of another being degenerate.

There is something different between all equal and all that have fixed ratio. Those are still in the class of non equal.

I think its a different way to see things or a different degeneracy perspective. I consider degenerate here the difference |a-b|.

There are no parallelograms in the real world anyway. So they are all degenerate in my theory of degeomtrization lol.


Call them non orthodiagonal parellelograms.

All parallelograms are simple, anyhow.

https://en.wikipedia.org/wiki/Simple_polygon

Okay.