En este episodio del Podcast Calculadora Alicia aprenderás a dividir fracciones paso a paso con el truco del inverso, simplificación y ejemplos prácticos, de forma clara y divertida.

Liu , π et la sagesse des polygones

Number of the Day - "347" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We explore A00331, the OEIS entry listing the coefficient of nu in the Rayleigh polynomial of even index 2n. From the numbers 5, 14, 1026, 4324 onward, we see a growth that encodes a deep link to the zeros of the Bessel function. We outline how these coefficients are constructed via standard formulas (psi_on and phi_pn) and why this sequence helps connect pure number theory to applied physics through Bessel zeros. We’ll also touch the historical trail—from Sloan’s Handbook to modern reference...

This week’s episode isn’t our usual deep dive—it’s a behind-the-scenes update. On Monday, Breaking Math vanished from Spotify, Apple, YouTube, and more without warning. After digging in, we discovered a strange RSS glitch that merged our feed with another podcast.In this quick update, Autumn shares: What happened behind the scenes when the show disappeared Which platforms are already fixed (and which we’re still waiting on) How you can make sure you never lose track of Breaking Math again What

Number of the Day - "346" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Number of the Day - "345" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We explore A000329, the tangent-iteration sequence defined by b(0) = 1 and the nearest integer to b(n), where b(n) = tan(b(n-1)). The interplay between the continuous, blow-up behavior of tan near odd multiples of π/2 and the discrete rounding step yields a surprisingly erratic sequence (with terms wandering through 1, 2, 75, -1, -1, -2 … and beyond). We unpack how the sensitivity of tan to its input, combined with rounding, acts as a powerful nonlinearity that can send the next term in a com...

Number of the Day - "344" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We dive into A000328, the Gaussian circle problem: how many integer lattice points (x, y) lie inside or on a circle of radius n. Start with the main term a(n) ~ πn^2 and the elusive remainder r(n) = a(n) − πn^2. We trace the historical bounds — Hardy and Landau showed the lower limit Ω(n^{1/2}); over the decades mathematicians sharpened the upper bound, with the current best known result due to Huxley giving a(n) − πn^2 = O(n^{131/208}) ≈ O(n^{0.6298}). We also connect to the sum-of-two-squar...

Number of the Day - "343" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Are you looking for Building Thinking Classrooms Style Math Tasks that are perfect for 2nd garde? In this episode, I talk about the best of the best, most popular second grade low-floor, high-ceiling math tasks!Have a topic you want me to discuss? Fill out the Google Form!Helpful Links2nd Grade Math Task Blog2nd Grade Bestselling Bundle2nd Grade Year-Long BundleTry a FREE Math TaskLet's Connect!InstagramWebsiteYouTube Channel

We explore A000327, the OEIS entry counting the number of solutions with distinct positive integers a and b to a^23 + b^23 ≤ n (i.e., partitions into non-integral powers). We trace its pedigree—from N. Sloan’s original listing in the 1973 Handbook of Integer Sequences to the expanded coverage in the 1995 Encyclopedia—and highlight its surprising connections beyond pure math, including Agarwala and Alok’s 1951 link to statistical mechanics. We unpack Seth Troisi’s neat formula that expresses A...

Number of the Day - "342" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

A deep dive into the pentagonal numbers A000326, tracing their geometric roots and arithmetic formula P(n) = n(3n−1)/2, including the pentagonal test x is pentagonal iff (sqrt(24x+1)+1)/6 is an integer. We explore generalized pentagonal numbers from negative n, Euler’s pentagonal number theorem and their role in partitions, and the striking links to primes: for any prime p>3, p^2−1 is divisible by 24 and corresponds to generalized pentagonal values. We’ll connect the geometry of dots formi...

Number of the Day - "341" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Thalès, celui qui mesura les pyramides

A000325 is the simple formula a_n = 2^n − n, with the start 1, 1, 2, 5, 12, 27, 58. It counts all subsets of an n‑element set except the n singletons (i.e., 2^n minus n). The sequence also satisfies the recurrence a_n = 2 a_{n−1} + (n−2) with a_0 = 1, leading to the clean closed form a_n = 2^n − n. In this episode we’ll unpack the intuition, derive the formula, and explore the various combinatorial interpretations and appearances of this compact, universal counting principle. Note: This podca...

Number of the Day - "340" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We explore a proposed standard that gives LLMs a concise, structured briefing about a website. llms.txt complements robots.txt and sitemaps by delivering AI-friendly guidance and links to detailed pages, all in a lightweight, human- and machine-readable format. Learn the required structure (site name in an H1, a brief abstract in a block quote, and H2 sections with name, URL, and description), plus an optional section for secondary info and practical tooling like llms.txt2txt. We discuss best...