Top all-time · #1276
Alexander Bogomolny
Personal blog · cut-the-knot.orgmathscience
Alexander Bogomolny writes Recent changes to Interactive Mathematics Miscellany and Puzzles, a personal blog at cut-the-knot.org about math and science. Since 2008, 58 different Hacker News readers have linked it 69 times, most often “Pythagorean Theorem and its many proofs”. It has a working feed you can follow.
Most-linked posts?
- Pythagorean Theorem and its many proofs3 people · 3 mentions · first linked 2015-07-19
- Interactive Mathematics Miscellany and Puzzles2 people · 2 mentions · first linked 2020-02-13
- /2 people · 2 mentions · first linked 2013-12-04
- Proofs of the Pythagorean Theorem2 people · 2 mentions · first linked 2023-03-25
- Cut the Knot: Interactive Mathematics Miscellany and Puzzles2 people · 2 mentions · first linked 2021-10-12
- A real life story: Factoring Polynomials2 people · 2 mentions · first linked 2008-03-01
- Calculation of the Digits of π by the Spigot Algorithm of Rabinowitz and Wagon2 people · 2 mentions · first linked 2018-03-14
- /pythagoras/index.shtml2 people · 2 mentions · first linked 2011-11-20
What Hacker News says?
Mathematics and Logic by Mark Kac and Stan Ulam (1992 Dover paperback, ISBN 978-0486670850) [1] Mathematics, Form and Function by Saunders Mac Lane (1986 Springer-Verlag hardcover, ISBN 0-387-96217-4) [2] [1]: https://www.cut-the-knot.org/books/kac/index.shtml [2]: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function
Comment linking /books/kac/index.shtml
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?”Submitted A seventh-grader student found a beautiful proof to Thales' Theorem (2002) as a story · 139 points
HN discussionThere are numerous books devoted to Olympiad preparation, there are websites completely devoted to Olympiads, there are freely available problems sets (with complete solutions). To name the few: Hungarian Problem Books, Problem-Solving Strategies, Challenging Problems in Algebra, books by Titu Andreescu - a former US IMO coach, who published a lot of books on math and IMO prep, http://www.cut-the-knot.org/
Comment linking /
on “Calculus For The People”Submitted Pi in Pascal's Triangle (2014) as a story · 68 points
HN discussionNotation is a pretty big deal in Mathematics. As software people we should be able to appreciate how evocative notation can get rid of unnecessary cognitive load when dealing with complexity. Here is a link that talks about notation in Maths: http://www.cut-the-knot.org/language/index.shtml . Here's another link: http://en.wikipedia.org/wiki/Nabla_symbol . The example from calculus is also pretty famous. Also, FWIW,…
Comment linking /language/index.shtml
on “No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)”Submitted Pythagorean Theorem and its many proofs as a story · 60 points
HN discussion> a feat considered impossible until they did it Hm? https://www.cut-the-knot.org/pythagoras/TrigProof.shtml > J. Zimba, On the Possibility of Trigonometric Proofs of the Pythagorean Theorem, Forum Geometricorum, Volume 9 (2009) And Zimba's proof terminates in a finite number of steps.
Comment linking /pythagoras/TrigProof.shtml
on “Teen mathematicians tie knots through a mind-blowing fractal”Submitted 12 Coins in Verse: Genius solution of twelve balls and a scale problem as a story · 31 points
HN discussionBrilliant. Reminds me of a similar site, though this one's more about demonstrating particular problems, rather than general concepts. http://www.cut-the-knot.org/
Comment linking /
on “World of Mathematics”Submitted Strategy and Tactics in Problem Solving as a story · 22 points
HN discussionIt's not an argument against government spending, nor was it intended as one. What makes you think so? It's an argument against this specific argument for government spending. Making bad arguments is excessively easy, independent of whether the thing argued for is good or bad, or true or false. To give a simple example: consider a faulty proof of Pythagoras' theorem. See eg https://www.cut-the-knot.org/pythagoras/Fa…
Comment linking /pythagoras/FalseProofs.shtml
on “U.S. Government Database of Dad Jokes”Submitted Math Lingo vs. Plain English: Double Entendre (1997) as a story · 13 points
HN discussionThe difference equation approach (computationally fastest) can be used to derive a elegant closed form solution that relates to the golden ratio. Fn=(1+√5)^n−(1−√5)^n\2^n√5 This deravation is pretty accessable and if you want to show off in code tests :) http://www.cut-the-knot.org/proofs/BinetFormula.shtml
Comment linking /proofs/BinetFormula.shtml
on “An integer formula for Fibonacci numbers”Submitted Perrin Sequence as a story · 7 points
HN discussionOk this nerd-sniped me pretty good, never seen this before and assumed it would be quickly connected to the Ulam spiral mentioned elsewhere in the the thread. That particular rabbit hole kinda bottoms out in polynomial residues and the very mysterious-sounding "Conjecture F" [0]. This parallax primes thing though led to the linked page [1] which has lots of background and other connections, including the most satisf…
Comment linking /Curriculum/Arithmetic/PrimesFromTriangle.shtml
on “Prime Number Grid”- mk · 2009-01-02
Submitted Interactive Mathematics Miscellany and Puzzles as a story · 6 points
HN discussion It's also the midpoint of the positive rationals, as modeled by the Stern-Brocot tree. https://www.cut-the-knot.org/blue/Stern.shtml
Comment linking /blue/Stern.shtml
on “1.5 is the midpoint between 0 and infinity in Ruby”Submitted Cut the Knot: Interactive Mathematics Miscellany and Puzzles as a story · 5 points
HN discussionI think you might like this: http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml
Comment linking /WhatIs/Infinity/9999.shtml
on “The Secret Number”Submitted Probability Paradoxes as a story · 5 points
HN discussionI think proof #6 on this page is easier to follow and uses the same similar triangles. But then it’s just some basic algebra without assuming anything about areas of similar triangles :) https://www.cut-the-knot.org/pythagoras/index.shtml#6
Comment linking /pythagoras/index.shtml
on “Garfield's proof of the Pythagorean Theorem”Submitted Surreal Numbers as a story · 4 points
HN discussionI think I've seen this before, except Feynman was going on about how circles aren't the only constant width shapes: http://www.cut-the-knot.org/Curriculum/Geometry/CWStar.shtml
Comment linking /Curriculum/Geometry/CWStar.shtml
on “If Richard Feynman applied for a job at Microsoft (2002)”Submitted A brief introduction to Rational Trigonometry as a story · 4 points
HN discussionWhat kind of proof? Here are 102 proofs of the Pythagorean Theorem. http://www.cut-the-knot.org/pythagoras/index.shtml
Comment linking /pythagoras/index.shtml
on “Who or What Broke My Kids?”Submitted Finicky Diophantine Equations as a story · 3 points
HN discussionThere is an extremely elegant solution to this modified question as well. In fact, it is always possible to fill a chessboard with dominoes with two squares of opposite color removed, by a very straightforward method (Gomory's Theorem). See Problem 2 at https://www.cut-the-knot.org/do_you_know/chessboard.shtml and note that the result generalizes to any bipartite Hamiltonian graph, such as any rectangular grid with…
Comment linking /do_you_know/chessboard.shtml
on “On the cruelty of really teaching computing science (1988)”Submitted Proofs of the Pythagorean Theorem as a story · 2 points
HN discussionA beautifully simple visual proof for sqrt(2): http://www.cut-the-knot.org/proofs/GraphicalSqRoots.shtml I recently coded up a visualization of the implied infinite descent, for sqrt(3): http://wry.me/toys/irrationaltriangle/
Comment linking /proofs/GraphicalSqRoots.shtml
on “Teaching Square Roots to a Five Year Old”Submitted Interactive Mathematics Miscellany and Puzzles as a story · 2 points
HN discussion
