Jekyll2023-12-02T03:25:11+00:00https://savirsingh.github.io/feed.xmlSavir SinghHi, I'm Savir Singh! I'm a high school student from Canada. I love developing software, creating new technologies, competitive programming, and math, just to name a few things.Savir Singhsavirsinghwork@gmail.com15 Fun Math Facts I’ve Collected2023-09-25T23:20:00+00:002023-09-25T23:20:00+00:00https://savirsingh.github.io/math/fifteenmathfacts<script type="text/x-mathjax-config">
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<h2 id="15-fun-math-facts-ive-collected">15 Fun Math Facts I’ve Collected</h2>
<h4 id="here-are-15-cool-math-facts-ive-collected-over-time">Here are 15 cool math facts I’ve collected over time.</h4>
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<h3 id="1-riemann-hypothesis">1. Riemann Hypothesis</h3>
<p>The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It concerns the distribution of nontrivial zeros of the Riemann zeta function, ζ(s).</p>
<h3 id="2-p-vs-np-problem">2. P vs. NP Problem</h3>
<p>The question of whether \(P\) (problems solvable in polynomial time) equals \(NP\) (problems whose solutions can be verified in polynomial time) is a major unsolved problem in computer science and mathematics.</p>
<h3 id="3-fermats-little-theorem">3. Fermat’s Little Theorem</h3>
<p>If \(p\) is a prime number and \(a\) is any integer not divisible by \(p\), then \(a^{(p-1)}\) is congruent to \(1 \space modulo \space p\).</p>
<h3 id="4-the-monster-group">4. The Monster Group</h3>
<p>The Monster Group is the largest sporadic simple group and has 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000, which is known as its order.</p>
<h3 id="5-kolmogorov-complexity">5. Kolmogorov Complexity</h3>
<p>Kolmogorov complexity measures the shortest program (in bits) needed to describe a particular object or piece of data. It’s used in algorithmic information theory.</p>
<h3 id="6-the-isoperimetric-problem">6. The Isoperimetric Problem</h3>
<p>The Isoperimetric Problem asks for the shape of a closed curve in the plane that encloses the maximum area. The answer is a circle.</p>
<h3 id="7-the-banach-tarski-paradox">7. The Banach-Tarski Paradox</h3>
<p>In three-dimensional space, it’s possible to decompose a solid sphere into a finite number of pieces and reassemble them into two solid spheres of the same size.</p>
<h3 id="8-the-collatz-conjecture">8. The Collatz Conjecture</h3>
<p>A deceptively simple problem in number theory, the Collatz Conjecture asks whether iterating a specific function will always reach the value 1 for any positive integer input.</p>
<h3 id="9-ramanujans-prime-number-formula">9. Ramanujan’s Prime Number Formula</h3>
<p>Srinivasa Ramanujan developed a remarkable formula for approximating the number of primes less than a given integer \(n\).</p>
<h3 id="10-the-birthday-paradox">10. The Birthday Paradox</h3>
<p>It’s counterintuitive but true that in a group of just 23 people, there’s a better-than-even chance that two people share the same birthday.</p>
<h3 id="11-the-four-color-theorem">11. The Four Color Theorem</h3>
<p>Proven with computer assistance, it asserts that four colors suffice to color any map so that no two adjacent regions have the same color.</p>
<h3 id="12-p-vs-bpp">12. P vs. BPP</h3>
<p>In computational complexity theory, BPP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time. The relationship between P and BPP is not fully understood.</p>
<h3 id="13-cantors-theorem">13. Cantor’s Theorem</h3>
<p>Cantor’s Theorem proves that there are more real numbers between 0 and 1 than there are natural numbers.</p>
<h3 id="14-the-basel-problem">14. The Basel Problem</h3>
<p>The Basel Problem, solved by Leonhard Euler, establishes that the sum of the reciprocals of the squares of the natural numbers converges to \(\frac{\pi^2}{6}\).</p>
<h3 id="15-gödels-incompleteness-theorems">15. Gödel’s Incompleteness Theorems</h3>
<p>Kurt Gödel’s theorems show that in any formal system of mathematics, there exist statements that are undecidable within that system.</p>
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<p>Thanks for reading! If you got this far, I hope you learned something cool. I found these facts to be quite interesting, which is why I decided to write this post about them.</p>Savir Singhsavirsinghwork@gmail.comUsing Thatformworks to make your HTML forms work2023-07-15T16:56:00+00:002023-07-15T16:56:00+00:00https://savirsingh.github.io/projects/thatformworks<h2 id="a-quick--simple-guide-to-getting-started-with-thatformworks">A quick & simple guide to getting started with Thatformworks</h2>
<h4 id="in-august-2022-i-started-a-project-that-once-complete-would-allow-me-to-make-html-contactreservation-forms-work-by-january-2023-i-completed-a-simple-working-version-of-this-project---and-decided-to-make-it-open-for-everyone-as-a-free-service-in-this-post-i-go-through-the-steps-to-use-thatformworks-to-make-your-html-forms-function-properly">In August 2022, I started a project that, once complete, would allow me to make HTML contact/reservation forms work. By January 2023, I completed a simple working version of this project - and decided to make it open for everyone as a free service. In this post, I go through the steps to use Thatformworks to make your HTML forms function properly.</h4>
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<h3 id="there-are-two-methods-you-can-choose-from-to-access-thatformworks">There are two methods you can choose from to access Thatformworks:</h3>
<ul>
<li>Send a request quickly and efficiently online.</li>
<li>Make a pull request and merge with the GitHub repository.</li>
</ul>
<p>I’d recommend the first option since I very rarely check for pull requests and merging it would be a lengthy process. On the other hand, sending a request online is very simple and will get your forms working in no time at all!</p>
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<h3 id="option-1---sending-an-online-request">Option 1 - Sending an online request:</h3>
<p>In order to send an online request, navigate to <a href="https://thatformworks.pythonanywhere.com">the Thatformworks website</a>. Next, type in your email address and submit the form! Soon, a team member will contact you regarding the setup of Thatformworks. It is usually a quick, free, and simple process.</p>
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<h3 id="option-2---creating-a-pull-request">Option 2 - Creating a pull request:</h3>
<p>In order to create a pull request, visit the <a href="https://github.com/savirsingh/thatformworks">GitHub repository</a> and make the request. It will likely take a long time to be reviewed and merged, which is why the first option is preferred.</p>
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<p>Thank you for reading this, and I hope it helped you!</p>Savir Singhsavirsinghwork@gmail.comA quick & simple guide to getting started with Thatformworks