History and Overview

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href=/list/math.HO/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 1 of 1 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2503.22620" title="Abstract" id="2503.22620"> arXiv:2503.22620 </a> [<a href="/pdf/2503.22620" title="Download PDF" id="pdf-2503.22620" aria-labelledby="pdf-2503.22620">pdf</a>, <a href="https://arxiv.org/html/2503.22620v1" title="View HTML" id="html-2503.22620" aria-labelledby="html-2503.22620" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.22620" title="Other formats" id="oth-2503.22620" aria-labelledby="oth-2503.22620">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Math Matters of the Past (The Very First Mathematical Olympiads) </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Fomin,+D">Dmitri Fomin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 18 pages; the Russian original was published in "Matematicheskoe Prosveschenie" magazine, issue 34 (2025); ISBN 978-5-4439-1907-2 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">History and Overview (math.HO)</span> </div> <p class='mathjax'> The history of the very first mathematical contests for high school students is discussed. The main body of the article is dedicated to the mathematical and scientific contests held in imperial Russia in the XIX century. More specifically, we discuss and analyze the recently discovered evidence of the city-level official "olympiads" in several school subjects (mathematics, history, and languages), which were organized in the Russian capital city of Saint Petersburg in 1840-1842. Educational and social aspects of the high school educational system of that time are discussed as well. </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 1 of 1 entries)</h3> <dt> <a name='item2'>[2]</a> <a href ="/abs/2206.07174" title="Abstract" id="2206.07174"> arXiv:2206.07174 </a> (replaced) [<a href="/pdf/2206.07174" title="Download PDF" id="pdf-2206.07174" aria-labelledby="pdf-2206.07174">pdf</a>, <a href="https://arxiv.org/html/2206.07174v4" title="View HTML" id="html-2206.07174" aria-labelledby="html-2206.07174" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2206.07174" title="Other formats" id="oth-2206.07174" aria-labelledby="oth-2206.07174">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Relations between $e$ and $蟺$: Nilakantha's series and Stirling's formula </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Irkhin,+V+Y">V. Yu. Irkhin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 6 pages, some explanations are extended </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">History and Overview (math.HO)</span> </div> <p class='mathjax'> Approximate relations between $e$ and $\pi$ are reviewed, some new connections being established. Nilakantha's series expansion for $\pi$ is transformed to accelerate its convergence. Its comparison with the standard inverse-factorial expansion for $e$ is performed to demonstrate similarity in several first terms. This comparison clarifies the origin of the approximate coincidence $e+2\pi \approx 9$. Using Stirling's series enables us to illustrate the relations $\pi^4+\pi^5 \approx e^6$ and $\pi^{9}/e^{8} \approx 10$.The role of Archimede's approximation $\pi=22/7$ is discussed. </p> </div> </dd> </dl> <div class='paging'>Total of 2 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.HO/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em">  <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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