memes siriusmart • 3 weeks ago • 87%

all nostalgia aside, arras.io is so much better

Daily Maths Challenges siriusmart • 1 month ago • 100%

Draw a hypocycloid using a graphical calculator (such as Desmos or Geogebra). Your hypocycloid should include - Inner circle of radius `a - Outer circle of radius `b - As time `t` increases the point on the inner circle should trace out the pattern, you can animate the graph using `t`. Below is the link to a Desmos graph: https://www.desmos.com/calculator/vzgog7xqrz

Daily Maths Challenges siriusmart • 2 months ago • 100%

- Given `n` and `m` are coprime, show that there exist integer `n'` such that `nn' mod m=1`. - The *extended Euclid's algorithm* is given below without proof, which may be useful in your proof. (I'm too lazy to type out the algorithm again, so look at the image yourself)

Daily Maths Challenges siriusmart • 2 months ago • 100%

- Prove that `z(x mod y) = (zx) mod (zy)` Be rigorous (trust me bro im gonna daily post trust me bro) EDIT: assume all variables are integers

Daily Maths Challenges siriusmart • 3 months ago • 100%

I recently started reading TAOCP, in other words you can expect daily posts from me again, because I'll just take some of the cooler questions from there and repost them here.

UKCasual siriusmart • 4 months ago • 87%

I'm a Londoner, I used to have this friend (who is *not* a Londoner) we had a huge disagreement on topic unspecified. But after I've watched this video I think I see his viewpoint, which is true. I just don't see it at all because there's such a enormous disconnect between London and the rest of the country. I would recommend you to watch the video as well, some arguments made in the video are slightly misleading, but the general picture is clear and true. https://youtu.be/b5aJ-57_YsQ

Daily Maths Challenges siriusmart • 4 months ago • 94%

S=sum of (-1)^n/n from 1 to infty For why I named the post as so, here's why ::: spoiler spoiler  :::

Daily Maths Challenges siriusmart • 4 months ago • 100%

- Show that `cosθ=(u⋅v)/(|u||v|)` for 2D vectors u and v. (it is quite hard to come up with these challenges, so if you got any ideas, please post them)

Daily Maths Challenges siriusmart • 4 months ago • 100%

It is not

Daily Maths Challenges siriusmart • 4 months ago • 100%

I've even got a starter question to get you guys into the scenario. Once you've completed the starter question, under the solution comment attaches the main question, which is unsolved.

Daily Maths Challenges siriusmart • 4 months ago • 100%

- Show that the infinite multiplication `(1+1/1)(1+1/2)(1+1/3)...` does not converge.

Daily Maths Challenges siriusmart • 4 months ago • 100%

- Show that if a function is differentiable for an interval, it is continuous over that interval. - A function is continuous if lim_x->a f(x) = f(a)

Daily Maths Challenges siriusmart • 4 months ago • 100%

- Express `y` in terms of `x` for differential equation `dy/dx=ylny` (I'm officially out of ideas again)

Daily Maths Challenges siriusmart • 4 months ago • 100%

- Show that it's possible `a^b=c` where `a` and `b` are irrational, and `c` is rational. Sry for the gap I ran out of ideas.

youtu.be

Have you seen this font before? This is Computer Modern and it's used everywhere from exams sheets to research papers, all because it is default font in popular typesetting language LaTeX, known for its ability to diplay maths equations, as well as being the de facto standard of writing articles in many fields of science. Which is surprising as LaTeX is a far less productive option compared to office suites, according to this study, it is much easier to make mistakes in LaTeX than word, something you don't want on a research paper. So how did it against all odds, become the favourite of scientific communities? Typesetting is the art of placing words on a page. Back in the 70s, it was usually done manually by professionals. However, this was not an option for Donald Knuth, as his publisher was too broke to afford one, instead they used computers to typeset his book, to which he was deeply dissatisfied with the poor results. Believing he can do better, he set out to create his own typesetting system for anyone to produce high-quality books with minimal effort. This was no easy feat, as the system will have to know the dimensions of all characters to find the optimal arrangement of characters per line, and lines per page. It took him 7 years of typography, and by 1978, he released the first version of TeX along with the Computer Modern font. After the initial learning curve, TeX slowly gained popularity among researchers. Soon words reached the American Math Society, who at the time was looking for a good digital typesetter. They quickly realised that TeX was exactly what they were looking for. Not only did they heavily promoted the use of TeX to members. Instead of waiting for new features to be added, they went ahead and extended TeX's ability to typeset maths using its powerful macro system, publishing the first ever macro package - AMSTeX. At the time TeX was able to produce high quality publications, but it was still very complicated to use. To make TeX accessible to everyone, 1984 LaTeX was created so macro packages such as AMSTeX can be used easily. This variant of TeX was so popular by 1990, it became the de facto standard in the scientific community. Since then LaTeX has been adopted by students for note taking, some markdown editors even include it as a proper way to display maths equations. On the flip side, vanilla LaTeX is still the favourite of many experienced users. And as I see it, there is nothing more fun than perfecting your notes to the point people like it more than the textbook. So have you hear of LaTeX before? What do you use LaTeX for? Let me know in the comments down below, anyways I'll be seeing you in two weeks, have a good one.

Daily Maths Challenges siriusmart • 4 months ago • 93%

- Show that the sum of the first `n` squares is `n(n+1)(2n+1)/6`. - I know this is often in the textbook for proof by induction, which is why proof by induction is *not* allowed. This is a relatively hard one, take your time.

Daily Maths Challenges siriusmart • 4 months ago • 88%

- Evaluate `SUM(1/(n + n^2))` from n = 1 to infty