Calvin Lin's messageboard

@Calvin Lin

Question

Does any know of a good contradiction that uses $\pi = \frac {22}{7}$?

Answer

By Euler's formula, $e^{-iy} = \cos (y) + i \sin (y)$

Let $\large x = i^i \Rightarrow \ln (x) = i \cdot \ln (i) = i \cdot i \cdot \frac {\pi}{2} \Rightarrow i^i = e^{-\pi/2}$

Similarly, let $\large x = (-i)^{-i} \Rightarrow \ln (x) = -i \cdot \ln (-i) = -i \cdot i \cdot -\frac {\pi}{2} \Rightarrow (-i)^{-i} = e^{-\pi/2}$

So $\large i^i = (-i)^{-i} = e^{-\pi/2}$

Suppose $\large \pi = \frac {22}{7}$

$\large i^i = e^{-11/7}$

$\large i^{7i} = e^{-11}$

$\large (i^7)^i = e^{-11}$

$\large (-i)^i = e^{-11}$

$\large (-i)^{-i} = e^{11} \ne i^i$ which is a contradiction. So $\pi \ne \frac {22}{7}$

Calvin Sir,what is the field of mathematics that you do your research on??

@Vishnudatt Gupta Please refrain from posting solutions which are directly copied off of another, or just a statement of the correct numerical answer. We have removed the solutions that you wrote in the past 5 days. If you continue to do so, we will take further action.

@Calvin Lin I have some questions for you....

1. Do you work from home or go to a Brilliant headquarter daily to work?

2. Did you find Brilliant or Brilliant found you?

3. What did you do before you met Brilliant?

4. Could you please suggest me some good learning material for maths?

@Sharky Kesa How Do You Solve This is an interesting question which echos the discussion that I had with @Finn Hulse in The Threes, where a kind of size argument is needed to prove that $x = y$.

Can one of you add a correct solution to this problem?

@Thaddeus Abiy Nice set of CS problems. How did you decide what problems to include?

Hi, this question just pop-up in my mind. What are the difference between you and the Best of NT, Algebra, etc.? Are there other people to control the Best of's?

@Calvin Lin , could you please do a note on Zsigmondy's theorem? I'd really love that!

How can we put an image while posting a solution???

Thanks for resharing my problem, Calvin :)

Sorry if you get this a lot and it's kinda spammy, but I wanted you to know I appreciate it, anyway.

Really looking forward to physics practice sections. Keep up the great work.

Cheers

Hi Calvin. Sorry to bother you with this, but I have a concern with the diagram that has been added to a question of mine. I always appreciate when diagrams are attached to my questions by the moderators, but in this case it does not match the parameters of the question and may prove to be a bit confusing to some. If at all possible, could a more accurate representation of the circles in question be supplied? Thanks for your help.

EDIT: Oh, I just checked the problem again and the diagram had been changed. That was a fast response! Thanks. :)

You're really great , Sir Calvin Lin! What do inspired you to educate talented students?

@Calvin Lin, can you tell me how to put 'image credits' like these? Well, you have posted great problems in Level 4 & Level 5 challenge sets. The weekly challenge set (of $24{th}$ March) was also a good one. Are you going to post more of these? Also when we write details & assumptions, it appears smaller in size. Please also tell me how to do that. (I am sorry if I am boring you with this!)

My Query

Image credit: There, and over there

Details and assumptions

Details and assumptions

@Finn Hulse Can you add your solution to What are Bob's chances of getting a cookie? Given that it has numerous tries and no correct as yet, I feel that your phrasing isn't sufficiently clear. There are some issues like:

1) What is 00:00 recorded as? Does it satisfy the conditions?
2) What is 00:10 recorded as? Does it satisfy the conditions?
3) I (reasonably) assume that seconds are not displayed?

The "Practice" section currently shows algebra only. Will the other topics appear soon?

@Sreejato Bhattacharya Nice set of geom problems.

Do me a favor, and select the topic and level as you create the problems. This helps us with the tagging and ratings :)

Can you please help me with this problem that I posted...I struggled with it for a long time and still failed to solve it. click here

Calvin, I see the picture you've put up for the "Stingy Rancher..." problem. I think you have a great sense of humor.

@Victor Loh That is a good set of NT questions. I would suggest that instead of placing all of the notes in the set, you simply provide a link to my/Arron's set. This way, others can more easily engage with the problems that you selected.

Mr. Calvin sir, may I ask? When will the "Challenge a Friend" option return? I'm not meaning to rush you or anything, I just wanted to know. :D

@Andrew Bai Any reason why you deleted your questions? They seem pretty interesting to me.

Suppose I've posted a problem that turns out to have a wrong "correct" answer. Rather than having to delete the question and start over, are you saying it's possible to ask the moderator to have the wrong "correct" answer changed to the actual correct answer? Provided if I myself report it and made the request?

$\pi$ is an irrational number , while $\frac{22}{7}$ is a rational number. !

Dear Calvin, a small query... is it possible in the future to have the old Brilliant problems in a separate link "Archive" for Brilliant Squared members. Presently there seems to be no organized way to access many of these interesting problems apart from a random search.

Dear Calvin, there is a geometry problem, "Tangent Circles" Level 5 posted by Nicotinamide Dinucleotide-Phosphate based on Descartes Theorem. I am getting an answer that is marked as incorrect which i am reasonably sure is correct. There does not seem to be any way of reporting this problem since there is no link for doing so with this problem. There is only one solver of this problem who is the originator of the the problem itself. Can you please have a look at your convenience? Thanks and regards. Satyen

How is it possible for this problem "Tangent Circles" by "Nicotinamide Dinucleotide-Phosphate" to have 4 Solvers, when the given correct answer only makes sense if the problem asks for $arctan\left( \sqrt { \frac { r }{ R } } \right) =y$ and not the way it's posted, asking for $arctan\left( \frac { r }{ R } \right) =y$? There's some kind of bug, I can't report the problem, and meanwhile I can't go look up the solutions or make a comment about solutions, so I have no idea what's going on. But the given correct answer was so curious that I've created another problem based on it, You can guess...

This is not the first time I've noticed that a problem posting an incorrect answer nonetheless getting a number of "Solvers", which only makes me scratch my head! I think we should always be able either post a solution or make a comment about solutions, even if we've blown the problem, because many times nobody gets around to posting a solution, but meanwhile the number of "Solvers" rack up.

Do you like carrots?

@Calvin Lin This is just a suggestion :) It would be betrer to have a confirmation box whenever a person wants to reveal a solution to the problem.

@Anuj Shikarkhane

Thanks for your numerous contributions to the Brilliant Wiki.

However, please refrain from copying directly from other sources, as that is a violation of intellectual property.

We have reverted your edits that were made in the past 2 weeks. This is your final warning. If you persist, we will take further action, like deleting your account.

Calvin

Hi Calvin. I just thought I should mention that there is an error in the second example of this wiki. If we were to apply Pythagoras directly to $\Delta ABD$ we would find that

$AD = \sqrt{84^{2} - 12^{2}} = 83.138$

to $3$ decimal places, as opposed to the given answer of $80$. I think that the problem is that, with the dimensions given, we can't have both $\angle ABC$ and $\angle BDC$ be right angles. This example has been posted on the Brilliant facebook page. :(

@Calvin Lin Quoting directly from the Vieta Root Jumping brilliant wiki page,

"If $a \geq b,$ let the other root be $c=\frac{b^2-k}{a}$. We have $c < \frac {b^2} {a} \leq b.$ If $c<0,$ then $c^2-kbc+(b^2-k)\geq c^2+k+b^2-k>0,$ which contradicts $c$ being the root of the equation. If $c=0,$ then $b^2=k,$ so $k$ is a perfect square and we are done. Otherwise, we can keep going, using $(b,c)$ instead of $(a,b)$. We get a decreasing sequence of positive integers $\{a_1,a_2,a_3,...\}=\{a,b,\frac{b^2-k}{a},...\}$ so that for all $n$ the pair$(a_n,a_{n+1})$ satisfies $\frac{a_n^2+a_{n+1}^2}{a_na_{n+1}+1}=k.$ Clearly, this sequence cannot continue indefinitely, so at some point one of the numbers will become $0,$ proving that $k$ is a perfect square. $_\square$"

The fact that $(a,b)$ satisfies the equation $\implies$ $(b,c)$ also satisfies the equation seems unjustified to me. Shouldn't it be that $(c,b)$ satisfies the equation or am I missing something. Also, does Vieta jumping apply only to symmetric polynomials? Looking forward to your reply.

Regards,
Sam.

@Arpit Sah This is Part 1, which happened before we decided to make a mini-series.

You could add in other "Proof without words" problems and posts by the Brilliant Community. I like @Mursalin Habib notes like Turn The Pencil Around.

@Zi Song Yeoh Oh gosh, your Trollathon problems are just cruel. I could do the first few, and then quickly got stuck.
I'm looking forward to attempting Trollathon 2 when I have time this weekend!

@Andres Badel Congrats on being the first to finish both Level 4 and Level 5 sets. Any words of encouragement for the rest?

Hey @Calvin Lin, what is that in your Tupperware container next to your laptop? Brain food?

@Calvin Lin I was looking at your recent Amphibious Car problem, and noticed that the graphic thingamajig had no image credit. Does this mean that you created it yourself, and if so, how? I could use some visual-creation website for my projects :)

@Tristan Shin Nice set on Formulas And Theorems! I'm glad I stumbled upon it.

Can you remove "Construction Time" from your set? You can do so by hovering over the item which would cause the "move" and "trash can" icons to appear, and then click the trash can. In the image below, you can see the icons in my 2th item.

Image

@Josh Rowley I actually think that dice sums 2 is harder than dice sums 3. You can apply @Rohit Singh 's insight in dice sums 1, which makes dice sums 3 pretty immediate.

@Robert Fritz What kind of new form of stupid assessment tests? The new SAT's?

Hi, @Calvin Lin, Can you look into this problem? The answer given is wrong and I don't know why it has got a rating. Also, contrary to the difficulty level of the problem, the rating given is ridiculously high. Thanks.

@Finn Hulse Please do not remove the flag from a problem unless you have dealt with it.

Let me know when you have clarified the phrasing of the problem Algotihmic Snowman, and I will remove the word "(wrong)" from the title.

@Finn Hulse There are many ways of saying something. The hard part is figuring out which way speaks exactly to you (since it would also depend on what you are familiar with). The harder part is figuring out which way speaks to the widest audience.

@Calvin Lin, have the 'best of' accounts been deleted? If it would be so, I would be horrified! Anyway, would we always get rated problems under the hash-tags?

@Calvin Lin, Cantor's continuum hypothesis had already faults in it & also, Gödel had proved that any theory with axiomatic definitions would be unstable. But, in my opinion, Mathematics is a language which appeals to our reasoning. But, it is hard to find a logical foundation to mathematics. What do you think?

@Finn Hulse I believe that you want to allow letters to repeat. If so, you should include that in the problem statement, otherwise I would assume that we're not allowed to repeat the letters.

@Calvin Lin : Are you aware that it is possible for regular members to solve b^2 practice problems by looking at other b^2 members' activities?

@Snehal Shekatkar @Abhijit Bendre I would be interested in reading a writeup to the general case of Where is that hen?

@Michael Diao Can you add a solution to Remainders oh remainders? Thanks.

Hi! I posted the following note on recurrence relations a few days ago containing a few problems am working with right now but didn't get any replies.....it will be extremely helpful if you give a few hints or reshare it for a wider audience Click here

@Calvin Lin - Please describe your journey to the IMO. How was it? How did you prep? What suggestions would you give to a weakling like me to achieve this status. And yes, please do answer @Satvik Golechha questions. They are also good.

@Calvin Lin Sir I would love to hear your opinion about this note Click Here

I'd want to know who is the guy in the picture?

@Calvin Lin, I need help! Which format is accepted? Looks like there is a fault in my PC. Try to help. Please.

why

Sir, Here is my note on Stochastic Programming.It will be extremely helpful for me if you write a small review of that note I mean in the sense how I can make it better.....I put a lot of effort into this one but it didn't get attention.

@Paul Ryan Longhas I've noticed that your 4 most recent problems have all been flagged for errors. Can you please review the disputes and update them accordingly? Otherwise I'd be deleting your questions.

@Anik Mandal In your problem Who should be the winner, I do not understand what you mean by "A bishop,threatens a square it is placed one."

@Krishna Ar RE techniques trainer, check out my sets, "Olympiad Algebra" etc, or Arron's sets "Algebra Techniques" etc.

Every once in a while I run into a nice problem, but end up being told that my answer doesn't fly. The normal recourse is to report it, and sometimes eventually the problem or the answer is changed. Wouldn't it speed things up if I'm able to forward a complete solution, so that nobody else has to duplicate the effort from scratch? This is a good case in point: Find the Distance...

Are Brilliant T Shirts still available?

@Jai Gupta , I do not see any significant edits made to this problem. The request is for you to state if the angle is in degrees or in radians.

Please check that you have received an email with regards to the clarification request. Thanks.

@Calvin Lin , thank you for reviewing the problem. That was a major screw-up on my part.

@Calvin Lin , I've a thing to ask you! Can you give me the link from where I can find the web page: "Challenges | Brilliant". Please?

I missed that solution 1+3+4=8. The other two 1+2+4=7 and 1+2+5=8 are impossibilities. I need to be out of town for a few days, so I had to delete the question and will repost it later.

Just a quick question: Im new to Brilliant and don't know if this is supposed to happen but 1 was level 2 in geometry and was demoted to level 1.

Where can you find your rating in different categories? I've been looking and still can't find it.

@Calvin Lin I liked the minor modifications done to the brilliant recently! But I want to point out two things: (1) If I add a new tag like #OlympiadMath to "My Topics" it doesn't appear in the topic list as before, so I've make a search for it again and again. Please fix it. (2) There's glitch here in grammar: When you visit a tag and point to "add to my topics", it's wrongly written as "Add to My Topics My Topics" @Finn Hulse

@Calvin Lin What was your experience with the IMO and what training did you do to get there?

@Calvin Lin @Finn Hulse I had recently shared a problem a day ago, but it still shows 0 posts in my stats! Please fix it!

@Calvin Lin, I liked the new format. But does that mean that Ratings are deleted permanently?

I know Brilliant is still working on points and ratings (Khim mentioned this a couple of weeks ago), but how is it decided which problems start out with 100 points and and which are stuck with 10 points? The "Christmas Tree Farm" is still at 10 points, even though over 100 people have looked at it with no solvers. I don't think it's a very difficult problem, but I'd like to understand better what makes posted problems stay in the netherworld of "10 point problems", so that I can better avoid designing problems that do that. My guess is that the problem has to be at least solved by some people, would that be right?

Christmas Tree Farm

Differential geometry was my favorite subject when I was in high school, so I have nostalgic memories for this kind of thing. I thought I'd share some ideas about it.

Sorry for bothering you with this, but I wasn't sure where else to ask this question. For the last couple of days the LaTeX code hasn't been converting properly for me, so all I see is a jumble of code. (It is still converting on other sites I frequent, however.) I can still "translate" most of the questions in my head, although it can be a slog sometimes, but I can't really post solutions anymore as I have no way of knowing if I have coded correctly. I can't recall doing anything on my end that would have led to this glitch. Do you have any ideas on how I can rectify this situation? Thanks in advance for your help.

Update: The LaTeX coding is converting again, so all is well. Still wondering whether the problem was with the site or my computer, since the problem seemingly just resolved itself.

How do you know how close you are to levelling up?

How do you post a direct link to something?

Calvin Edit: This is a link to your profile

What would be possible if humans used 100% of their brain power?

This is a recurring problem. When posting a problem, how do you review the "Attached Image" and adjust the size of it before it's posted? After it's posted, I'm forced to delete the problem if I want to make changes to the attached image. I have a hard time predicting how large the final image will be, given the image file I use.

In my problem Evildoer's Plot-Part 2 shows the answer as something that I didn't put in. Is it because ten-thousandths are too small for it or would it take that answer as well?

@Calvin Lin , can you please fix up the typo I created in my problem Parallelogramania? I forgot one of the 'L's in the title. I profusely hate typos. Thanks

My set SUGAR CUBE PUZZLE still has problems that do not have a level. Can you please give them a level?

Did Brilliant get updated? If so, can you please tell me the new updates?

@Calvin Lin I've always wondered about one thing: when we report problems, can we use $\LaTeX$ and [website] (www.example.com) and bold, italic text while we type? Can you see all these elaborate writing styles?

There might be a bug in reporting a problem with this one

The hardest integral ever!!

I've tried reporting the fact that the “correct answer” expression numerically works out to 0.597385197... while the definite integral works out to 0.597381809..., which means that the "answer" of "11" is misleading. It implies there is an exact mathematical expression for this definite integral. At least it's not that one, as given. But something is preventing me from reporting this problem? Can't get through.

@Harshvardhan Mehta There was a submitted dispute which explains why the answer was changed. Please check that you receive emails from us.

Can anyone tell me what parts of Brilliant got updated? Thanks

If you solve a level 3 problem but later it becomes level 5, do your points increase or stay the same?

@Yan Yau Cheng Can you check if this problem was from the JOMO, and if so, is the given answer the same as yours?

I have some concerns about this problem.

The reason I ask is because it has been tagged with JOMO.

sir, how to transform an improper integral with positive / negative infinity as its limits into 1 and 0 limits? I'm currently investigating on Kac's formula. thanks a lot!

Sir, how to determine the height of a density function? its too bad I can't post the function... thanks a lot!

https://brilliant.org/profile/jerwin-6ttgor/sets/for-later/142682/kac-formula/#

I don't know any contradiction but I had to report something, my approx. 30,000 points are cut for the reason I don't know and I solved the problem named its more than a pully but it says you did not solve the question. My answer was correct. Pls. help

Thanks for getting back to me regarding my disputed question. It would have been such a mess to fix that I decided to just delete it and post a similar question here employing the same concept but which could be solved "on the back of an envelope". Thanks again for following up.

I do not know where I should put Brilliant related questions so I put it here. Apology in advance.

I just created a new note named 'Matter as Waves' and saved it in a set. Now, it does not appear in the feeds or explore, except it just appears in that Set. What do I do to make it behave in a normal way so that all my followers can see it?

I've been wondering.. Is it difficult to remove the little bug that makes any comment always receive an upvote from the creator of the comment himself? I am surprised it is still there.

So, I was just posting a solution to my new problem, and just before publishing, I saw a typo, so I clicked "Keep Private" instead of "Publish". Now it's just gone, I can't see it at all, nor can I post a new solution. Is there a way to recover my private solution, and make it public?

@Steven Zheng @DEEPANSHU GUPTA @Diego E. Nazario Ojeda @bj prognome Can you check if you received an email from me in the past week? Thanks!

do you know your iq???

@Calvin Lin why are my comments are being deleted? my comment on Expanding the wiki were also deleted!!!!!!!!!!!!!!!! Why?? what's the matter?

@Calvin Lin sir I am not receiving any mail from brilliant , as I run brilliant by facebook and not by gamail my gmail id is plohomi123@gmail.com

Sir @Calvin Lin , I have had some trouble with geometry, I´m level 4 because trigonometry problems :D but I still have great difficulty to answer level 3 or 4 problems. What should I do? What do you recommend me to study?

Okay, yet another bug report. Lately, I haven't been getting any email notices from Brilliant, and now I see that one of my recently posted problems is being flagged. But I have no idea what the message is.

Mighty Mosquito

My usual email address is Scythian@aol.com

Calvin (and Silas), I hate to say this, but Brilliant.Org has been blacklisted by AOL for reasons given by an AOL tech that make little or no sense. I gave the AOL tech a hard time about this, but he really does not know what's going on, it's over his head. So, you guys will have to follow up with AOL to clear this. This link is what it takes to get whitelisted by AOL.

AOL Whitelist

@Calvin Lin Hello, I have recently shared a problem. However, I forgot to assign it the level, and now I have published it. Is there anyway I can assign it a level now? I wanted it to be a level 3.

Thanks.

Sir Calvin, can you suggest me the title of the topics regarding roots of the polynomials? I encountered a lot of problems as such to roots of polynomials and simplifying the values.. However I cannot simplify them because of the imaginary number.. Can you help me Sir?

@Isaac Jacobs Integer answers are not restricted to lying in the range 0 to 999. Note that we also allow for decimal answers.

Hi Calvin. I notice that you left a comment to my comment on Christopher Boo's solution to this question. The problem is that I'm unable to access any of the comments to his solution. This glitch shows up every once in a while, and normally after a few refreshes and/or some scrolling the comments finally show, but this time the comments seem to be permanently hidden. It's also odd that comments to other posted solutions appear, but not to Christopher's. I don't know if the problem can be rectified, but I just thought I'd let you know that it has occurred. Regards, Brian.

Sir could you please check and say what is wrong with this sum in the link below

https://brilliant.org/community-problem/is-this-math-or-what-itmw-3-infinity-is-even-or-2/?group=v3iGwCQZUA4A

@Venture HI @Mark Mottian @Kevin Mo @John Ashley Capellan Can you check if you received an email from me last week? Thanks!

@Calvin Lin , do you know about some study material of finance and budgeting?

Yo Calvin just out of curiosity.. Is it possible to allow communication between members? I have seen some great people here from my country with whom I want to get in touch with!! If you say no, no hard feelings.

BRILLIANCE IS OUTCOME OF brilliant.org :P

Hi Calvin. I just had an odd experience with LaTeX. I had written a solution to this question a few hours back, and then just now had a look at it and noticed a minor typo. So I made the edit and submitted the revised solution, but then the formatting suddenly became a mess. So I went back into edit mode and found that multiple back-slashes had been added throughout the solution. I went through and erased them as best I could, re-submitted, and then the solution ended up looking even worse than before. I swear back-slashes were being added even while I was editing. I felt like the Sorcerer's Apprentice. Anyway, I gave up and deleted my solution for good, but I wanted to let you know of the event in case there might be some glitch or virus that might need to be addressed. I don't think it's at my end, but I can't be sure. I'm also a bit hesitant about submitting any more solutions until I know what happened here.

@Trevor Arashiro @Kyouhei James Do you guys know each other???

You're both 15 and from Honolulu!

@sudoku subbu Thanks for contributing so many problems. Please do not type in all capital letters, as that represents that you are shouting on the internet.

Sir, could you please make sure that the questions whose level's are pending are tended to a bit quicker than the current speed. A lot of questions that I've posted haven't been assigned a level and some of my very easy problems for which I've suggested a level 1 marking have a tag of 100 points and now everyone gets it right to get a free 100 points. With all due respect sir, please attend to this matter. I'm pretty sure that even others are facing this problem, right?

Sir I want to share problems on my gmail account so that more of my friends comes here , only 3 of my friends are here one is vraj mehta , pranav nair and vivek joshi - out of them only vraj mehta log in once in 3-4 days

If I share problems(by clicking it , it directly lands up to sign up box) and it looks like this , I think it will attract many, I have shared some of the problems in my photo album too but only sharky kesa have seen it

Sir sorry to disturb you , having an odd experience with posting a problems -

See the screenshot,

I posted now a question but same thing happened , I deleted one , That's OK

SIR CAN I GET TO KNOW WHATS ABOUT THE MODULO FUNCTION ...PLSSSSSSSSSSS

IS GOOGLOPLEXIAN THE WORLDS LARGEST NUMBER?????????????????

how to check our subject rating?

i live in kota india not in banglore india

Hi Calvin,

My classmate, Victor Loh, as you may know is a moderator. If u dunno, we both study in your Alma Mater secondary(RI), so I would like to know the criterion(a) to become a moderator! thnks!

Guess I failed to apply Mrs Soh's English (if u noe what I mean) =)

Has anybody besides myself ever made 1000+ comments?

calvin sir how much do you earn