diff --git a/ipynb/Beal.ipynb b/ipynb/Beal.ipynb index c52c667..2e60a2d 100644 --- a/ipynb/Beal.ipynb +++ b/ipynb/Beal.ipynb @@ -28,7 +28,7 @@ ">
where $A, B, C, x, y, z$ are positive integers and $x, y, z$ are all greater than $2$, \n", ">
then $A, B$ and $C$ must have a common prime factor.\n", "\n", - "[Andrew Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles) proved Fermat's theorem in 1995, but Beal's conjecture remains unproved, and Beal has offered [\\$1,000,000](http://abcnews.go.com/blogs/headlines/2013/06/billionaire-offers-1-million-to-solve-math-problem/) for a proof or disproof. I don't have the mathematical skills of Wiles, so I could never find a proof, but I can write a program to search for counterexamples. I first wrote [that program in 2000](http://norvig.com/beal2000.html), and [my name got associated](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=beal%20conjecture) with Beal's Conjecture, which means I get a lot of emails with purported proofs or counterexamples (many asking how they can collect their prize money). So far, all the emails have been wrong. This page catalogs some of the more common errors and updates my 2000 program." + "[Andrew Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles) proved Fermat's theorem in 1995, but Beal's conjecture remains unproved, and Beal has offered [$1,000,000](http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize) for a proof or disproof. I don't have the mathematical skills of Wiles, so I could never find a proof, but I can write a program to search for counterexamples. I first wrote [that program in 2000](http://norvig.com/beal2000.html), and [my name got associated](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=beal%20conjecture) with Beal's Conjecture, which means I get a lot of emails with purported proofs or counterexamples (many asking how they can collect their prize money). So far, all the emails have been wrong. This page catalogs some of the more common errors and updates my 2000 program." ] }, { diff --git a/ipynb/Convex Hull.ipynb b/ipynb/Convex Hull.ipynb index b9822f3..de6c550 100644 --- a/ipynb/Convex Hull.ipynb +++ b/ipynb/Convex Hull.ipynb @@ -36,7 +36,7 @@ "\n", "- *Every point in **P** lies either on or inside of **H**.*\n", "- *Every vertex of **H** is a point in **P**.*\n", - "- **H** *is convex: a line segment joining any two vertexes of **H** either is an edge of **H** or lies inside **H**.*\n", + "- **H** *is convex: a line segment joining any two vertexes of **H** either is an edge of **H** or lies inside **H**.*\n", "\n", "\n", "In this notebook we develop an algorithm to find the convex hull (and show examples of how to use `matplotlib` plotting). The first thing to do is decide how we will represent the objects of interest:\n", diff --git a/ipynb/Sicherman Dice.ipynb b/ipynb/Sicherman Dice.ipynb index 41b8b9b..9b1c6a4 100644 --- a/ipynb/Sicherman Dice.ipynb +++ b/ipynb/Sicherman Dice.ipynb @@ -1100,7 +1100,7 @@ "source": [ "Now, what do we have to do for `all_dice(N)`? When we knew we had six sides, we wrote six nested loops. We can't do that for *N*, so what do we do?\n", "\n", - "**Here's an iterative approach: we keep track of a list of partially-formed dice, and on each iteration, we add a side to all the partially-formed dice in all possible ways, until the dice all have `N` sides. So for eaxmple, we'd start with:**\n", + "**Here's an iterative approach: we keep track of a list of partially-formed dice, and on each iteration, we add a side to all the partially-formed dice in all possible ways, until the dice all have `N` sides. So for example, we'd start with:**\n", "\n", " dice = [(1,)]\n", " \n",