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

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## Comments

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TopNewest@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 :)

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

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Woot! Thanks!

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Divisibility Rules? @Tan Kenneth and @Sharky Kesa contributed a clear writeup. I will start from there, and then explore further.

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:)

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My pleasure :)

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

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

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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.

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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)

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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 :)

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

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

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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?

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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!

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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.

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

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