Top Mathematics discussions
NishMath - #Geometry
|
gasarch (noreply@blogger.com)@Computational Complexity
//
Two high school students have achieved a remarkable feat by discovering a novel proof of the Pythagorean Theorem. This new proof, which employs trigonometry, has been accepted for publication after undergoing rigorous scrutiny. The achievement is particularly noteworthy because proving the Pythagorean Theorem using trigonometry is challenging due to the potential for circular reasoning, as trigonometry itself relies on the Pythagorean Theorem. Despite this hurdle, the students' proof has been deemed valid, showcasing their mathematical ingenuity.
The Pythagorean Theorem, a cornerstone of geometry and trigonometry, has been found on clay tablets dating back to 1770 BCE. These tablets, predating Pythagoras by over 1,000 years, reveal that ancient Babylonian mathematicians were aware of the theorem and used it to solve problems. One tablet, IM 67118, demonstrates the application of the theorem to calculate the diagonal length of a rectangle. Another tablet shows a square with triangles and markings, illustrating their understanding of the relationship between the sides of a square and its diagonal. This historical evidence challenges the traditional attribution of the theorem solely to Pythagoras. The newly discovered proof by the high school students and the revelation of the theorem's ancient origins highlight the enduring relevance and evolving understanding of mathematics. While the students' proof demonstrates fresh perspectives on a classical theorem, the historical context emphasizes that mathematical knowledge is often developed and disseminated over centuries and across cultures. As mathematician Bruce Ratner notes, the Babylonians were likely familiar with the Pythagorean Theorem and irrational numbers well before Pythagoras, suggesting a rich and complex history of mathematical discovery.
Share:
References :
Classification:
Sophia Wood@Fractal Kitty
//
The 238th Carnival of Mathematics is now available online at Fractal Kitty, rounding up math blog posts from March 2025. This edition, organized by Aperiodical, features a variety of math art and explores interesting facts about the number 238, including that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime." The Mathstodon community contributed fun facts about 238, such as its relation to Uranium-238 and its representation in hexadecimal as "EE."
The carnival includes a variety of blog posts and activities from around the mathematical community. Peter Cameron shared thoughts on Compactness, Memories of CFSG, and defending research against government censorship, while other posts covered topics like polyominoes, a modern presentation of Peano Axioms, and the Monty Hall Problem. Karen Campe continued her visual Go For Geometry Series, and Amédée d’Aboville explored Group Theory With Zoombinis. These diverse topics showcase the breadth of interests and engagement within the math world. Beyond traditional blog posts, the carnival highlights creative endeavors like Ayliean's #MathArtMarch, which showcased crochet, coding, painting, and other artistic expressions inspired by mathematics. There's also discussion happening on platforms like Mathstodon, with Terence Tao sharing insights on dynamical systems and the complexities of linear versus nonlinear regimes. Pat's Blog delves into geometry, discussing properties of rhombuses and extensions of concurrency theorems, demonstrating the vibrant and varied nature of mathematical discussions and explorations.
Share:
References :
Classification:
@primes.utm.edu
//
This week saw a flurry of mathematical activity, highlighted by the 238th Carnival of Mathematics, organized by Aperiodical. The carnival showcases a variety of submissions and mathematical art, focusing on the number 238 itself. Noteworthy facts about 238 include that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime". The carnival also encourages exploration beyond pure mathematics, with community members contributing insights linking the number to uranium isotopes, birth minutes, and even hexadecimal representations. It also shines a light on #MathArtMarch, with examples of crochet, coding, and painting from around the world.
Continuing the daily exploration of numbers, several interesting facts and events were highlighted for April 6th, 7th, 8th and 10th. The number 96, the 96th day of the year, was examined for its unique properties, such as being the smallest number expressible as the difference of two squares in four different ways. Events like Euler's first paper on partitions (April 7th, 1741) and Al-Biruni's observation of a solar eclipse in 1019 were also noted, linking mathematical concepts to historical contexts. Also, the number 97 has been noted as the 97th day of the year, where 97 is the largest prime that we can ever find that is less than the sum of square of its digits. In recreational mathematics, a "Salute" game for reinforcing multiplication and division was featured, emphasizing the inverse relationship between these operations. Additionally, the concept of "truncatable primes" was explored through a game where players create strings of prime numbers by adding digits to either end of a number. The number 91 was discussed as the 91st day of the year where 10 n + 91 and 10 n + 93 are twin primes for n = 1, 2, 3 and 4. Finally, highlighting mathematics beyond academia, James Abram Garfield, a former Congressman and mathematician, was mentioned for his original proof of the Pythagorean Theorem, illustrating the interdisciplinary nature of mathematics.
Share:
References :
Classification:
|
Blogs
|