Nov 4 Great Wiki Submissions

Nov 4 Great Wiki Submissions from the past week

The Brilliant Community has contributed wonderfully to the Wiki. Here are some of the best articles submitted over the past week:

Level 1-2

(Algebra) Induction - By Mursalin Habib, Aditya Virani and Samuraiwarm Tsunayoshi

(Geometry) Section Formula - By Beakal Tiliksew and Christopher Boo

(Calculus) Applying Differentiation Rules to Exponential Functions - By Mahindra Jain, Aditya Virani and Thiago Baldissarelli

Level 3-5

(Algebra) Graphing Rational Equations - By Chung Kevin

(Geometry) Conics - Parabola - Focus and Directrix - By Pranshu Gaba and Aditya Virani

(Number Theory) Fermat’s Little Theorem - By Asama Zaldy, Satvik Golechha and Mursalin Habib

(Algebra) Roots of Unity - By Mei Lam and Jubayer Nirjhor

(Number Theory) Extended Euclidean Algorithm - By Thaddeus Abiy, Agnishom Chattopadhyay and Anuj Shikarkhane

The following Wiki Pages that could use your help. Add to the explanations, or provide further examples.

Pythagorean Theorem - Started by Hamza Waseem and Goh ZhiJie

Tangent Line at a Point - Started by Tan Jun Wei

Analyzing Inelastic Collisions - Started by Anuj Shikarkhane

Menelaus’ Theorem - Started by Tan Kenneth

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}

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

@Mursalin Habib @Aditya Virani @Samuraiwarm Tsunayoshi @Beakal Tiliksew @Christopher Boo @Mahindra Jain @Thiago Baldissarelli @Chung Kevin @Pranshu Gaba @Asama Zaldy Jr. @Satvik Golechha @Mei Lam @Jubayer Nirjhor @Thaddeus Abiy @Agnishom Chattopadhyay @Anuj Shikarkhane @Hamza Waseem @ZhiJie Goh @Tan Jun Wei @Tan Kenneth

Thanks! I enjoyed reading your contributions :)

Calvin Lin Staff - 6 years, 7 months ago

My pleasure :)

Agnishom Chattopadhyay - 6 years, 7 months ago

Hamza Waseem - 6 years, 7 months ago

Sir, I have submitted wiki on division algorithm and a proof in wiki of primes from integers section.

shivamani patil - 6 years, 7 months ago

Woot! Thanks!

@Calvin Lin – sir, can u give some tips or tricks , how to approach divisibility related problems?

Nihar Mahajan - 6 years, 7 months ago

@Nihar Mahajan – Are you familiar with Divisibility Rules? @Tan Kenneth and @Sharky Kesa contributed a clear writeup. I will start from there, and then explore further.

I think it would be nice if Brilliant had a wiki on inequalities, considering that they are one of the most popular types of problems selected for olympiads. thoughts? @Calvin Lin P.S. can anyone submit an article for the wiki? (obviously keeping in mind the wiki guidelines)

Aritra Jana - 6 years, 7 months ago

Check out the Classical Inequalities section. There have been some writeups that are incoming for these articles. I will be featuring them in the upcoming weeks, when there are more examples. You can chip in by adding some basic examples to these too :)

I have added a wiki on "applications of Cauchy schwarz" ..It is still incomplete though...

@Aritra Jana – Thanks! No worries, there will be other members like you who will add their input, making this a great page soon :)

@Aritra Jana – @Aritra Jana I have also added some information on Cauchy Schwarz. If you want, you may choose to read it.

Anuj Shikarkhane - 6 years, 7 months ago

Pls insure proper solutions for the respected problems.give the solutions also........

Yogesh Borate - 6 years, 7 months ago

There are a lot of examples, with problems included, in the writeups. We are excited that the community is helping out by contributing examples here and there :)

Sometimes, I decide to add "additional problems" at the end of the wiki writeup, especially if there is no practice section. This will allow you to review the material and practice directly.

I would love reading a post on functional equations and how to tackle them!

Satyam Bhardwaj - 6 years, 7 months ago

The wiki on induction is extremely well-done. But I was wondering why they said "Before we sign off,let's see induction at action one more time" right before the last problem. Doesn't it make it look like the posters don't want anyone else to edit the post?

Rahul Saha - 6 years, 7 months ago

Hmm... It does seem that way. No worries! You can edit that sentence out if you want. Or you can add stuff before that sentence. If you think you can improve an article by making an edit, by all means do that!

Mursalin Habib - 6 years, 7 months ago

The writeup is extremely well-done.I was wondering if someone could add the "making the induction hypothesis stronger"-type problems.For example,

Prove that $(1+\dfrac{1}{1^3})(1+\dfrac{1}{2^3}).......(1+\dfrac{1}{n^3})<3$ for all positive integers $n$ .

In the above example,one has to make the induction hypothesis stronger by changing the right side to $3-\dfrac{1}{n}$ and changing the $<$ sign to $\le$ . I have never really understood the motivation behind doing so.

@Rahul Saha – You are talking about induction by strengthening the hypothesis (or as Calvin likes to call it "stronger induction") and it has its own wiki entry. No one's contributed to it yet and I plan to do that as soon as possible.

The motivation comes from experience and observation [this sentence is both truthful and unhelpful at the same time].

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}`	$\boxed{123}$