What are /r/CasualMath's favorite Products & Services?

From 3.5 billion Reddit comments

Some comments:

• It's not really an equation, is it?
• You can cancel the powers of x in the numerator and denominator.
• "x" is really two completely different things here, by the look of it; the "x" appearing in the powers is presumably not just 0, whereas the independent variable that y depends on is zero.

Please see this: https://www.overleaf.com/read/mxwdbdsdhvmm

That last sum looks simple, but Wolfram can't tell me what it is, and I feel as though I'd've seen it before if it had some generally recognisable value in terms of the function. Obviously, it's got a value for any polynomial... but I'm not sure what else to suggest.

This example allows the shockwaves to propagate at different speeds. You can set r*1* and r*2* equal (like this) for a demo that is more applicable to most real-world problems. This is also more useful if you are trying to teach students about conic sections (as enforcing equal propagation guarantees a conic section, save degenerate forms).

Linear algebra can act as a "transition" course between high school and university mathematics. It's very practical (full of operations and algorithms used in geometry, image processing, machine learning and more that can be implemented on a computer), but abstract at the same time (it gives you definitions and axioms and makes you reason about them to prove theorems).

This is a free online linear algebra course taught from the perspective of a computer scientist/programmer: https://www.coursera.org/course/matrix

You can also look around at Math Doctor Bob's video page (note that there are several tabs) for different university-level math topics and see if anything catches your interest.

I made a thing.

It simulates two players playing war with a 52 card deck (4 suits). It has them face off for 100 games keeping track of who wins and how long the game lasted. At the end, it prints out the average number of rounds as well as the minimum and maximum number of rounds.

You can change the two variables at the top (card_count and suit_count) to mess around with different sized decks.

Here is the graph with several more b values computed numerically.

Unfortunately it doesn't scale with changes to the initial values like yours does. That would be super cool, but I've already spent too much time on this haha. Algebraic solutions to those quartics would give you that.

Also, if you zoom in on intersections of the larger ellipses, you can tell there's some numerical errors going on, but what can you do.

Super cool! Thanks for posting about this!!

Thank you, WhyDoIRedditSoMuch. A thorough but accessible explanation. This has continued to blow my mind for years. Khan makes a pretty good case for its mind-blowingness as well.

If you rearrange the equation such that b = 2^x - 3^x , you can see quite clearly that b has an infinite number of possible values, represented by the graph shown here.

So what, specifically, are you looking for?

The number one book in "popularity" is a Harry Potter book. Its popularity number is 1. It's "Members" number is the highest for any book in Library Thing, 77,872.

I'm guessing there's some book whose Popularity = 5000 and its Members=5000, or something like that.

The numbers are kind of inversely related, as Popularity goes up Members goes down.

I took a whole course on this in college!

Here's a good start: https://en.wikipedia.org/wiki/Integer_factorization#Factoring_algorithms

I can also recommend the textbook "Factorization and Primality Testing" by Bressoud.

By the use of the word "difference" it sounds like you may have stumbled on what is known as the calculus of finite differences.

Martin Gardner has a great article on the calculus of finite differences that may help you understand it a little better.

You can't take the inverse cosine of -2. The cosine function ranges from -1 to 1. Thinking of the inverse cosine as "for what angle is cosine = -2" you realize you can't do it.

Here's a graph,

Check over your work, you'll probably find some simple mistake. I always drop negatives, or add when I'm meant to subtract...

edit: more accurately you can take arccosine(-2) However, it is a complex number in the imaginary plane. Not what I think you are looking for.

This is a website that does all of that for you, correctly, AND uploads the result to the bitcoin blockchain as a cryptographically verifiable 'public place' (reddit could, theoretically at least, be back-dated. The bitcoin blockchain cannot)

http://www.proofofexistence.com/

Edit: apparently that website requires you to pay them the bitcoin to add it to the blockchain. It's like a nickel, so if you actually want to do it, PM me and I'll pay it for you.

Haha nice. I was actually thinking about big numbers since reading about Graham's number yesterday, and how when you get to a certain size what really matters is the number of digits because after a while things aren't really "bigger than each other" in a meaningful way as much as they're all just "big". Then I thought I wonder what it looks like to graph out how big every number is compared to the one that came before it, and when I saw the graph I knew I had to know the exact point where the graph turned.

The reason this does not work is because it is an indeterminate form.

Observe that sec^(n)x only converges for (as n tends to infinity) all x = 2*πk* for integer k and all other x diverge.

Now if we add a coefficient that tends to zero we can try to counteract this. Some coefficients, such as 1/(log*n*+1) are insufficient and some tend to zero too quickly, such as 1/n, and do cause it to tends towards 1.

If you do some algebra, you can find a coefficient that will always force the equation to equal 2 when x=1 and equal to 1 when x=0. Here is a graph to play with these different choices of coefficients to help visualize why it is indeterminate.

Do you have the solver add-in for Excel?

I made a quick solution there if you want to look at a way to solve it, another way would be to make an equation for the cost, and minimize it with respect to the constraints by formulating a Lagrangian equation.

Link to Excel file

THAT IS PERFECT. Thanks!

I believe the 'fixed point' then for this site's ranking is about 2500.

There are about 2 million members and about 8 million books. Thanks again. Exactly what I was looking for.