RadMaths

Welcome to RadMaths! We will update popular maths problems and discussions to help you learn, think more and advance in Maths.
Physics to be included in MadPhysics :)

list of 1000 primes - FOR NORMAL USERS
list of primes to a million(78498 primes) - FOR CODERS

COURSES:
Calculus

LATE EVENTS:
approximating a slice of pi
simplifying trigonometric values into (nested) radicals

Problems:
- Alice Smith
1. SAT 1000 series
2. Luogu series
3. reach the summit series
4. Integration Grandmaster series
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
- Zakir Husain
1. Pre-RMO questions
2. The e-day quiz
- Jeff Giff
1. Dr Fiendish series
1,2,3,4
- Aryan Sanghi
1. When two lines meet series
2. Coordinate geometry series
- Valentin Duringer
1. Dynamic Geometry series
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43-sequel to 42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60

Discussions:
- Zakir Husain
1. On area percentage series
1,2,3-bonus
2. Math also fails series
1,2
3. Recurring decimals
- Yajat Shamji
1.Recurring proof notes
See Recurring decimals.
2. Number spy challenges
1,2
- Gandoff Tan
- Vinayak Srivastava
1. 10 PRMO sample questions-discussion
2.PRMO discussion
- Páll Márton (A Former Brilliant Member)
1. Proof chain
- Jeff Giff
1. Bilingual geometry note
- Inquisitor Math
1. A function whose reciprocal is an inverse

Formatting:
- Brilliant
1. LaTeX\LaTeX formatting guides
- Percy Jackson
1. LaTeX\LaTeX formatting guides
- Daniel Liu
1. LaTeX\LaTeX formatting guides
- Hamza Anushath (Frisk Dreemurr)
1. LaTeX\LaTeX formatting guides
- Páll Márton (A Former Brilliant Member) THIS IS THE BEST. SAVE IT NOW.
1. LaTeX\LaTeX formatting guides

Note by Jeff Giff
8 months, 1 week ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

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Top Newest

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It doesn't work.

Percy Jackson - 4 weeks ago

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But it is working in my PC Right now!

Zakir Husain - 4 weeks ago

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@Zakir Husain Ya, it works now, I submitted :)

Percy Jackson - 4 weeks ago

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Nice and very simple quiz

10/1010/10 for the interesting thought for making the question

Frisk Dreemurr - 4 weeks ago

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Ah but I can’t access it in mainland China :P

Jeff Giff - 3 weeks, 6 days ago

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e

A new one!

Zakir Husain - 3 weeks, 6 days ago

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@Zakir Husain I suppose I’m the only person still awake yet I cannot access to Google! :P

Jeff Giff - 3 weeks, 6 days ago

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@Zakir Husain Nice quiz! Can you tell me how to solve the second last one? Rest of them felt like I have seen them somewhere in Physics, even though I haven't learnt them in math! Especially the last one, it reminded me directly of equation of a wave. Guessed a few by elimination.

Vinayak Srivastava - 3 weeks, 6 days ago

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@Vinayak Srivastava Solution of second last one (with standard notations) : bn+1=bn(1an)b_{n+1}=b_n(\frac{1}{a}-n) =bn1(1a(n1))(1an)=b_{n-1}(\frac{1}{a}-(n-1))(\frac{1}{a}-n) =(1an)(1a(n1))...(1a1)1a=k=0n(1ak)=(\frac{1}{a}-n)(\frac{1}{a}-(n-1))...(\frac{1}{a}-1)\frac{1}{a}=\prod_{k=0}^{n}(\frac{1}{a}-k) bn+1=k=0n(1ak)\Rightarrow b_{n+1}=\prod_{k=0}^{n}(\frac{1}{a}-k) bn=k=0n1(1ak)\therefore b_{n}=\prod_{k=0}^{n-1}(\frac{1}{a}-k) bnan=ank=0n1(1ak)\Rightarrow b_na^n=a^n\prod_{k=0}^{n-1}(\frac{1}{a}-k) =k=0n1a(1ak)=\prod_{k=0}^{n-1}a(\frac{1}{a}-k) =k=0n1(1ak)=\prod_{k=0}^{n-1}(1-ak) lima0bnan=lima0k=0n1(1ak)\therefore\lim_{a\to 0} b_na^n=\lim_{a\to 0} \prod_{k=0}^{n-1}(1-ak) =k=0n1lima0(1ak)=k=0n11=1=\prod_{k=0}^{n-1}\lim_{a\to 0}(1-ak)=\prod_{k=0}^{n-1}1=1 lima0bnan=1\therefore\lim_{a\to 0}b_na^n=1 lima0bnann!=1n!\therefore \red{\lim_{a\to 0}\frac{b_na^n}{n!}}=\frac{1}{n!} lima0n=0bnann!=n=0lima0bnann!\lim_{a\to 0}\sum_{n=0}^{\infty}\frac{b_na^n}{n!}=\sum_{n=0}^{\infty}\red{\lim_{a\to 0}\frac{b_na^n}{n!}} =n=01n!=e=\sum_{n=0}^{\infty}\frac{1}{n!}=e

Zakir Husain - 3 weeks, 4 days ago

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@Zakir Husain Wow! Wonderful to see how it collapses after the limit! Loved the solution! :)

Vinayak Srivastava - 3 weeks, 3 days ago

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Could any of you make this a quiz or problem set on brilliant? Thanks!

Jeff Giff - 3 weeks, 3 days ago

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Sure

Zakir Husain - 3 weeks, 3 days ago

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@Jeff Giff - You can use buttons in RadMaths to make it more rad. See my note Buttons to learn button formatting :)

Percy Jackson - 6 months, 3 weeks ago

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I used it in anther note :) I don’t think it is necessary to add buttons here :)

Jeff Giff - 6 months, 3 weeks ago

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Nice, @Jeff Giff

Yajat Shamji - 8 months, 1 week ago

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What about my Recurring Proof Notes? You think they are useful to your note, @Jeff Giff?

Yajat Shamji - 8 months, 1 week ago

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@Jeff Giff- Try my A Pre-RMO question! series, Math also Fails! series.

Zakir Husain - 8 months, 1 week ago

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That's a definite one for @Jeff Giff to try - the Pre-RMO questions.

Also, RMO stands for...?

Yajat Shamji - 8 months, 1 week ago

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By the way, try this for Math Also Fails - eiπ=1,(eπ)i=1,e^{i\pi} =-1, (e^\pi)^i =-1, then i=logeπ1?!i=\log_{e^\pi} -1?!

Jeff Giff - 8 months ago

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No actually, definition of log clearly states that logablog_ab is defined only when

  • a>0anda1a \gt 0 and a \neq 1

  • b>0b \gt 0

Aryan Sanghi - 8 months ago

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Well it is correct, and not surprising if you know the Taylor series of ln\ln and this

Zakir Husain - 8 months ago

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If you want a big and detailed explanation you can ask for that (can even write a note!)

Zakir Husain - 8 months ago

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Oops.. that’s logarithm for negative numbers :/

Jeff Giff - 8 months ago

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Good idea! I’ll add them :)

Jeff Giff - 8 months, 1 week ago

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@Jeff Giff, Thanks for the mention for my LaTeX\LaTeX{} Guide but, it is a work in progress and I can suggest you better ones - Daniel Liu's Guide and Hamza Anushath's Guide.

Percy Jackson - 8 months ago

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Ok! Thanks!

Jeff Giff - 8 months ago

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Thanks for the mention of Mathathon 2020 too!

Percy Jackson - 8 months ago

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And please add mine too @Jeff Giff (I am Hamza Anushath)

Frisk Dreemurr - 8 months ago

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@Frisk Dreemurr @Hamza Anushath - He still didn't add your Latex note, LOL

Percy Jackson - 7 months, 2 weeks ago

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@Percy Jackson Yeah, it has been two weeks @Percy Jackson @Jeff Giff

Frisk Dreemurr - 7 months, 2 weeks ago

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@Frisk Dreemurr Correction - 2 weeks and 3 days LOL

Percy Jackson - 7 months, 2 weeks ago

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@Frisk Dreemurr Mathathon started, start posting solutions @Hamza Anushath

Percy Jackson - 7 months, 2 weeks ago

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@Percy Jackson Yeah, if I post solutions for past questions, will I still get points @Percy Jackson

Deduct five points from the total due to late submission if you'd like as well

Frisk Dreemurr - 7 months, 2 weeks ago

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@Frisk Dreemurr Cuz I didn't see the Mathathon problems till just now @Percy Jackson...

Frisk Dreemurr - 7 months, 2 weeks ago

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@Frisk Dreemurr No deduction for past questions go post the solutions!

Percy Jackson - 7 months, 2 weeks ago

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@Percy Jackson Thnx @Percy Jackson!

Frisk Dreemurr - 7 months, 2 weeks ago

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Try my When two lines meet series, it is a series of hard questions for learning to solve questions using graph. Is this useful for your note?

Aryan Sanghi - 8 months ago

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@Jeff Giff Add this sreies also, of @Aryan Sanghi

Zakir Husain - 8 months ago

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Thanks a lot @Zakir Husain

Aryan Sanghi - 8 months ago

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@Aryan Sanghi Thanks to @Jeff Giff for adding this in the note

Zakir Husain - 8 months ago

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@Zakir Husain Yes, @Jeff Gift great initiative this is like Percky Jackson.

Aryan Sanghi - 8 months ago

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@Jeff Giff Also try to add polyfon series by @Aryan Sanghi

Zakir Husain - 8 months ago

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Yes,thanku. I'll try to make the polyfun series more vast by adding more problems to it.

Aryan Sanghi - 8 months ago

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@Jeff Giff- Kindly mention this note instead of my feed for Pre-RMO question series.

Zakir Husain - 8 months ago

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👌 OK!

Jeff Giff - 8 months ago

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@Jeff Giff, could you add my note\color{#333333}\text{add my note} too as a LaTeX\LaTeX guide, it has many new facts and features which may only have been mentioned by me

Frisk Dreemurr - 8 months ago

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Click the add my note\text{add my note} to access my note @Jeff Giff

Frisk Dreemurr - 8 months ago

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@Jeff Giff, if you need anything from me, check out my profile and choose the series (i.e. if you choose one problem, you have to have the rest of the problems with that title.)

Yajat Shamji - 8 months ago

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@Jeff Giff - Kindly add this in RedMaths ''Late Events''

Zakir Husain - 7 months, 3 weeks ago

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@Jeff Giff Thanks!

Zakir Husain - 7 months, 3 weeks ago

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Check this out, @Páll Márton :)

Jeff Giff - 7 months, 2 weeks ago

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Thank you!

A Former Brilliant Member - 7 months, 2 weeks ago

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@Jeff Giff What about this?

Zakir Husain - 7 months, 1 week ago

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Wowie!!!!!! RadMaths has become even better! Good work @Jeff Giff! You'll have to organize it a bit though, like removing the Mathathon as it is over, adding more space between 2 different series, etc.

Percy Jackson - 7 months, 2 weeks ago

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@Jeff Giff it is Vinayak Srivastavsa not Yinayak @Vinayak Srivastava ?

Zakir Husain - 7 months, 1 week ago

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Yes @Jeff Giff!

Vinayak Srivastava - 7 months, 1 week ago

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Uh oh. Typo ^@^

Jeff Giff - 7 months, 1 week ago

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@Jeff Giff, check out this:

Magic Square Connections Study

Yajat Shamji - 7 months, 1 week ago

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@Jeff Giff you might like to add my Coordinate geometry series. All of its questions are popular and level 5. :)

Aryan Sanghi - 5 months, 1 week ago

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The link is level 4 actually lol

Percy Jackson - 5 months, 1 week ago

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Yes, this question didn't live to the expectations, but it's atleast popular. :)

Aryan Sanghi - 5 months, 1 week ago

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@Aryan Sanghi Yes, it is a very good problem. I like all your problems, they are new and different, pretty cool according to me.

Percy Jackson - 5 months, 1 week ago

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@Percy Jackson Thanku very much for your appreciation. :)

Aryan Sanghi - 5 months, 1 week ago

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@Jeff Giff, I think the actual PRMO discussion is this, so please change the link, that one has only sample questions. :)

Vinayak Srivastava - 3 weeks, 3 days ago

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very nice collection. thank you

num IC - 2 weeks, 2 days ago

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Hey everyone! I just found a way to nest buttons!!! All we have to do is to quote in a button and make a button in the quote! Only we can’t nest tables :( @Frisk Dreemurr , @Yajat Shamji
Test: (Failed)

[[show-hide-button|+]] [[start-hidden]] whoa I can button comments [[end-hidden]]

Jeff Giff - 1 week, 2 days ago

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Páll Márton would love this awww... but he is removed :(

Jeff Giff - 1 week, 2 days ago

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You used > to make a quote right

Jason Gomez - 5 days, 12 hours ago

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How did you make it, I can create the nested button but can’t hide stuff in it

Jason Gomez - 4 days, 22 hours ago

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@Jason Gomez Oh I forgot! You have to put the nested button frame behind the last button instead of in it :P I found that by accident actually and it turns out you can’t put line breaks though :)

Jeff Giff - 4 days, 14 hours ago

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Is it okay if I remake this note to make it more... accessible? I will give credit + link to this note as well if you do

Frisk Dreemurr - 1 week, 2 days ago

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Ok :) but a better way would be to link this note in the daily problem solutions :) or would you just want the code for this note?

Jeff Giff - 1 week, 1 day ago

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You see, num IC has accessed this note from my daily solution :)

Jeff Giff - 1 week, 1 day ago

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Look:

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Welcome to RadMaths! We will update popular maths problems and discussions to help you learn, think more and advance in Maths.   
**_[list of 1000 primes](https://brilliant.org/discussions/thread/list-of-primes/)_**          
**_COURSES:_**        
[Calculus](https://brilliant.org/discussions/thread/calculus-notes/?ref_id=1610121)      
**_LATE EVENTS:_**          
[approximating a slice of pi](https://brilliant.org/discussions/thread/least-operations-and-numbers-possible/?ref_id=1610787)    
[simplifying trigonometric values into (nested) radicals](https://brilliant.org/discussions/thread/how-to-find-trigonometric-values-that-radical/)

**Problems:**     
*- Alice Smith*     
1. [SAT 1000 series](https://brilliant.org/discussions/thread/sat-1000-problems-series-upcoming-frequently/)   
2. [Luogu series](https://brilliant.org/discussions/thread/luogu-problem-set/)         
3. [reach the summit series](https://brilliant.org/discussions/thread/reach-for-the-summit-problem-set-mathematics/)           
*- Zakir Husain*    
1. [Pre-RMO questions](https://brilliant.org/discussions/thread/a-pre-rmo-question-whole-series/)       
2. [The e-day quiz](https://brilliant.org/discussions/thread/happy-e-day/)    
*- Jeff Giff*    
1. Dr Fiendish series    
   [1](https://brilliant.org/problems/dr-fiendish/?ref_id=1591979),[2](https://brilliant.org/problems/dr-fiendish-2/?ref_id=1592533),[3](https://brilliant.org/problems/dr-fiendish-3/?ref_id=1592894),[4](https://brilliant.org/problems/dr-fiendish-4/?ref_id=1593218)   
*- Aryan Sanghi*       
1. [When two lines meet series](https://brilliant.org/problems/when-two-lines-meet-7/)            
2. [Coordinate geometry series](https://brilliant.org/problems/ellipses-circular-mask/?ref_id=1602635)      
*- Valentin Duringer*    
1. Dynamic Geometry series     
   [1](https://brilliant.org/problems/dynamic-geometry-level-1/?ref_id=1610351),[2](https://brilliant.org/problems/dynamic-geometry-level-2/?ref_id=1610354),[3](https://brilliant.org/problems/dynamic-geometry-level-3/?ref_id=1610360),[4](https://brilliant.org/problems/dynamic-geometry-level-4/?ref_id=1610363),[5](https://brilliant.org/problems/dynamic-geometry-level-5/?ref_id=1610385),[6](https://brilliant.org/problems/dynamic-geometry-level-6/?ref_id=1610388),[7](https://brilliant.org/problems/dynamic-geometry-level-7/?ref_id=1610400),[8](https://brilliant.org/problems/dynamic-geometry-level-8/?ref_id=1610408),[9](https://brilliant.org/problems/dynamic-geometry-level-9/?ref_id=1610427),[10](https://brilliant.org/problems/dynamic-geometry-level-10/?ref_id=1610469),[11](https://brilliant.org/problems/dynamic-geometry-level-11/?ref_id=1610472),[12](https://brilliant.org/problems/dynamic-geometry-level-12/?ref_id=1610475),[13](https://brilliant.org/problems/dynamic-geometry-level-13/?ref_id=1610479),[14](https://brilliant.org/problems/dynamic-geometry-level-14/?ref_id=1610541),[15](https://brilliant.org/problems/dynamic-geometry-level-15/),[16](https://brilliant.org/problems/dynamic-geometry-level-16/),[17](https://brilliant.org/problems/dynamic-geometry-p17/?ref_id=1610607),[18](https://brilliant.org/problems/dynamic-geometry-p18/?ref_id=1610617),[19](https://brilliant.org/problems/dynamic-geometry-p19/?ref_id=1610772),[20](https://brilliant.org/problems/dynamic-geometry-p20/?ref_id=1610775),[21](https://brilliant.org/problems/dynamic-geometry-p21/?ref_id=1610872),[22](https://brilliant.org/problems/dynamic-geometry-p22/?ref_id=1610875),[23](https://brilliant.org/problems/dynamic-geometry-p23/?ref_id=1610878),[24](https://brilliant.org/problems/dynamic-geometry-p24/?ref_id=1610891),[25](https://brilliant.org/problems/dynamic-geometry-p25/?ref_id=1610903),[26](https://brilliant.org/problems/dynamic-geometry-p26/?ref_id=1610909),[27](https://brilliant.org/problems/dynamic-geometry-p27/?ref_id=1611231),[28](https://brilliant.org/problems/dynamic-geometry-p28/?ref_id=1611234),[29](https://brilliant.org/problems/dynamic-geometry-p29/?ref_id=1611237),[30](https://brilliant.org/problems/dynamic-geometry-p30/?ref_id=1611356),[31](https://brilliant.org/problems/dynamic-geometry-p31/?ref_id=1611359),[32](https://brilliant.org/problems/dynamic-geometry-p32/?ref_id=1611389),[33](https://brilliant.org/problems/dynamic-geometry-p33/?ref_id=1611393),[34](https://brilliant.org/problems/dynamic-geometry-p34/?ref_id=1611396),[35](https://brilliant.org/problems/dynamic-geometry-p35/?ref_id=1611399),[36](https://brilliant.org/problems/dynamic-geometry-p36/?ref_id=1611402),[37](https://brilliant.org/problems/dynamic-geometry-p37/?ref_id=1611409),[38](https://brilliant.org/problems/dynamic-geometry-p38/?ref_id=1611471),[39](https://brilliant.org/problems/dynamic-geometry-p39/?ref_id=1611474),[40](https://brilliant.org/problems/dynamic-geometry-p40/?ref_id=1611483),[41](https://brilliant.org/problems/dynamic-geometry-p41/?ref_id=1611486),[42](https://brilliant.org/problems/dynamic-geometry-p42/?ref_id=1611536),[43-sequel to 42](https://brilliant.org/problems/dynamic-geometry-p43/?ref_id=1611539),[44](https://brilliant.org/problems/dynamic-geometry-p44/?ref_id=1611544),[45](https://brilliant.org/problems/dynamic-geometry-p45/),[46](https://brilliant.org/problems/dynamic-geometry-p46/)                

**Discussions:**     
*- Zakir Husain*     
1. On area percentage series      
    [1](https://brilliant.org/discussions/thread/on-area-percentage/?ref_id=1593918),[2](https://brilliant.org/discussions/thread/on-area-percentage-2/?ref_id=1594187),[3-bonus](https://brilliant.org/discussions/thread/on-area-percentage/?ref_id=1593918)   
2. Math also fails series      
    [1](https://brilliant.org/discussions/thread/math-also-fails/?ref_id=1590442),[2](https://brilliant.org/discussions/thread/math-also-fails-2/?ref_id=1592912)       
3. [Recurring decimals](https://brilliant.org/discussions/thread/on-recurring-decimals/)    
*- Yajat Shamji*          
1.Recurring proof notes    
    See [Recurring decimals](https://brilliant.org/discussions/thread/on-recurring-decimals/).    
2. Number spy challenges          
    [1](https://brilliant.org/discussions/thread/number-spy-challenge-1/),[2](https://brilliant.org/discussions/thread/number-spy-challenge-2/)     
[*- Gandoff Tan*](https://brilliant.org/profile/gandoff-5e56fk/)            
*- Vinayak Srivastava*          
1. [10 PRMO sample questions-discussion](https://brilliant.org/discussions/thread/prmo-sample-questions/)          
2.[PRMO discussion](https://brilliant.org/discussions/thread/prmo-discussion/)       
*- Páll Márton (A Former Brilliant Member)*             
1. [Proof chain](https://brilliant.org/discussions/thread/math-prove-marathon/)           
*- Jeff Giff*           
1. [Bilingual geometry note](https://brilliant.org/discussions/thread/bilingual-geometry-notebook/?ref_id=1598123)         
*- Inquisitor Math*        
1. [A function whose reciprocal is an inverse](https://brilliant.org/discussions/thread/a-function-whose-reciprocal-is-an-inverse/)    

**Formatting:**     
*- Brilliant*   
1. [\\\(\\LaTeX\\\) formatting guides](https://brilliant.org/math-formatting-guide/)      
*- Percy Jackson*    
1. [\\\(\\LaTeX\\\) formatting guides](https://brilliant.org/discussions/thread/latex-formatting-guide/)    
*- Daniel Liu*     
1. [\\\(\\LaTeX\\\) formatting guides](https://brilliant.org/discussions/thread/beginner-latex-guide/)       
*- Hamza Anushath (Frisk Dreemurr)*           
1. [\\\(\\LaTeX\\\) formatting guides](https://brilliant.org/discussions/thread/different-types-of-latex-formatting-methods-that-i/)            
*- Páll Márton (A Former Brilliant Member)*         
1. [\\\(\\LaTeX\\\) formatting guides](https://brilliant.org/discussions/thread/formatting-guide/) 

Jeff Giff - 1 week, 1 day ago

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@Jeff Giff, the deed is done. Check out my latest note!

Frisk Dreemurr - 22 hours ago

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@Frisk Dreemurr @Jeff Giff mention[10101485:Jeff Giff]

Frisk Dreemurr - 22 hours ago

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@Frisk Dreemurr Sorry, just wanted to get your mention number tag :)

Frisk Dreemurr - 22 hours ago

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@Frisk Dreemurr Check my new mentions page then, here

@Frisk Dreemurr mention[10427613:Frisk Dreemurr] (I need to add your mention Id)

Jason Gomez - 22 hours ago

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@Frisk Dreemurr nice!

Jeff Giff - 15 hours ago

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Line 25 may be my worst creation (holy cow I didn’t click enter) :P

Jeff Giff - 1 week, 1 day ago

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