RadMaths

Welcome to RadMaths! We will update popular maths problems and discussions to help you learn, think more and advance in Maths.
Science(and programming!) to be included in MadScience :)
MATHATHON by Percy Jackson
Mathathon 2020
Mathathon 2021

list of 1000 primes - FOR NORMAL USERS
list of primes to a million(78498 primes) - FOR CODERS (aware:may take 1 minute to load)

COURSES:
Calculus
Science

LATE EVENTS:
approximating a slice of pi
approximating a slice of pi - remade
Finding number of prime factors

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
3. It’s Mathematics Olympiad series
  1,2,3
Jeff Giff
1. Dr Fiendish series
  1,2,3,4
2. 13-year-olds’ homework in China(the hard problems) set
Aryan Sanghi
1. When two lines meet series
2. Coordinate geometry series
Valentin Duringer
1. Dynamic Geometry series
  1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48, 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91, 92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
  129,130,131,132,133,134,135,136,137.
  Notes have been published on this series:see discussions part.
Nihar Mahajan
1. Calculator is for the dull series
  1,2-credits to a former brilliant member,3-credits to Zakir Husain,4-credits to Zakir Husain,5-credits to Zakir Husain
Aman Rajput
1. Hot Integrals!
  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
Tomislav Franov
1. Tomi’s challenges
  1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21

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
2. On translating trigonometric identities to (nested) radicals!
Chew-Seong Cheong
1. On Dynamic Geometry series
  On Q32,77,89,94,98, On Q80,85,90,99,105, On Q96,101,106,109,111,112

Formatting:

Brilliant
1. $\LaTeX$ formatting guides
Percy Jackson
1. $\LaTeX$ formatting guides
Páll Márton (A Former Brilliant Member)
1. $\LaTeX$ formatting guides

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
list


1. numbered
2. list

numbered
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"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

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/)

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.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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Top Newest

Quiz

@Vinayak Srivastava @Mahdi Raza @Percy Jackson @Jeff Giff @Aryan Sanghi @Yajat Shamji

Zakir Husain - 4 months, 2 weeks ago

It doesn't work.

A Former Brilliant Member - 4 months, 2 weeks ago

But it is working in my PC Right now!

Nice and very simple quiz

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

Frisk Dreemurr - 4 months, 2 weeks ago

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

Jeff Giff - 4 months, 2 weeks ago

A new one!

Now it started! @Vinayak Srivastava @Mahdi Raza @Frisk Dreemurr @Aryan Sanghi @Yajat Shamji @Siddharth Chakravarty

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

@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.

Vin_Math 91 - 4 months, 2 weeks ago

@Vin_Math 91 – Solution of second last one (with standard notations) : $b_{n+1}=b_n(\frac{1}{a}-n)$ $=b_{n-1}(\frac{1}{a}-(n-1))(\frac{1}{a}-n)$ $=(\frac{1}{a}-n)(\frac{1}{a}-(n-1))...(\frac{1}{a}-1)\frac{1}{a}=\prod_{k=0}^{n}(\frac{1}{a}-k)$ $\Rightarrow b_{n+1}=\prod_{k=0}^{n}(\frac{1}{a}-k)$ $\therefore b_{n}=\prod_{k=0}^{n-1}(\frac{1}{a}-k)$ $\Rightarrow b_na^n=a^n\prod_{k=0}^{n-1}(\frac{1}{a}-k)$ $=\prod_{k=0}^{n-1}a(\frac{1}{a}-k)$ $=\prod_{k=0}^{n-1}(1-ak)$ $\therefore\lim_{a\to 0} b_na^n=\lim_{a\to 0} \prod_{k=0}^{n-1}(1-ak)$ $=\prod_{k=0}^{n-1}\lim_{a\to 0}(1-ak)=\prod_{k=0}^{n-1}1=1$ $\therefore\lim_{a\to 0}b_na^n=1$ $\therefore \red{\lim_{a\to 0}\frac{b_na^n}{n!}}=\frac{1}{n!}$ $\lim_{a\to 0}\sum_{n=0}^{\infty}\frac{b_na^n}{n!}=\sum_{n=0}^{\infty}\red{\lim_{a\to 0}\frac{b_na^n}{n!}}$ $=\sum_{n=0}^{\infty}\frac{1}{n!}=e$

Zakir Husain - 4 months, 1 week ago

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

Vin_Math 91 - 4 months, 1 week ago

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

Jeff Giff - 4 months, 1 week ago

Sure

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

A Former Brilliant Member - 10 months, 2 weeks ago

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

Jeff Giff - 10 months, 2 weeks ago

Hi @Tomislav Franov , your problem set has been included to this note! Good job! :)

Jeff Giff - 1 month, 1 week ago

Hi, thank you so much!!!

Tomislav Franov - 1 month, 1 week ago

Nice, @Jeff Giff

Yajat Shamji - 11 months, 3 weeks ago

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

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

Zakir Husain - 11 months, 3 weeks ago

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

Also, RMO stands for...?

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

Jeff Giff - 11 months, 3 weeks ago

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

$a \gt 0 and a \neq 1$
$b \gt 0$

Aryan Sanghi - 11 months, 3 weeks ago

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

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

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

Good idea! I’ll add them :)

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

A Former Brilliant Member - 11 months, 3 weeks ago

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?

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

👌 OK!

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

Frisk Dreemurr - 11 months, 3 weeks ago

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

@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 - 11 months, 2 weeks ago

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

Zakir Husain - 11 months, 2 weeks ago

@Jeff Giff Thanks!

Zakir Husain - 11 months, 1 week ago

Check this out, @Páll Márton :)

Jeff Giff - 11 months ago

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.

A Former Brilliant Member - 11 months ago

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

Zakir Husain - 11 months ago

Yes @Jeff Giff!

Vin_Math 91 - 11 months ago

Uh oh. Typo ^@^

@Jeff Giff, check out this:

Magic Square Connections Study

Yajat Shamji - 11 months ago

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

Aryan Sanghi - 8 months, 4 weeks ago

The link is level 4 actually lol

A Former Brilliant Member - 8 months, 3 weeks ago

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

Aryan Sanghi - 8 months, 3 weeks ago

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

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

very nice collection. thank you

num IC - 4 months ago

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 - 3 months, 3 weeks ago

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

You used > to make a quote right

Jason Gomez - 3 months, 3 weeks ago

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

@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 :)

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 - 3 months, 3 weeks ago

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?

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

Look:

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

Frisk Dreemurr - 3 months, 2 weeks ago

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

@Jeff Giff Kindly add this

Zakir Husain - 3 months, 1 week ago

Done :)

Jeff Giff - 3 months, 1 week ago

@Jeff Giff Add this in bold

Zakir Husain - 2 months, 3 weeks ago

@Jeff Giff Can you add these?

Calculator is for the dull - 5, Calculator is for the dull - 4, Calculator is for the dull - 3, Calculator is for the dull - 2, Calculator is for the dull - 1, It's Mathematics Olympiad! - 3, It's Mathematics Olympiad! - 2, It's Mathematics Olympiad! - 1, Trigonometry Everywhere - 2, Trigonometry Everywhere - 1

These are not by me (those in bold)

Zakir Husain - 2 months, 2 weeks ago

@Jeff Giff ????

@Jeff Giff What about "It's Mathematics Olympiad" ? and "Trigonometry Everywhere" ?

Zakir Husain - 2 months, 1 week ago

@Zakir Husain – At work now :) I’m quite busy :P

Jeff Giff - 2 months, 1 week ago

Oh I wasn’t noticed! Now I see :)

Jeff Giff - 2 months, 2 weeks ago

Thanks for all that!

Have you edited the note? I am not able to see them right now...

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$