conversations.from: human
conversations.value: Give me a description for a book titled Professor Stewart's Hoard of Mathematical Treasures about Stuffed, Professor, Cabinet with the genre: Humor & Entertainment, Puzzles & Games.
conversations.from: assistant
conversations.value: Stuffed with puzzles, jokes, word problems, puns, and history and lore about math, this sequel to Professor the authors Cabinet of Mathematical Curiosities (2009) reads like a numbers guy performing stand-up comedy (A piece of a string walked into a bar...). An old hand at the routine, the authors contention that his compendium can entertain anyone with math-class memories is amply borne out, and his ability to surprise is one reason. One never knows whats next: a proof that two plus two indeed equals four jostles with a spoof of proof itself. To keep readers on their toes, or at least flipping back to his superlative storehouse of sneaky solutions, the author flummoxes them with bizarre propositions, such as two plus two actually equals zerowhen youre doing modular arithmetic. Speaking of equality, the equal sign makes for a go-to topic for amusing vignettes, while stories about math underlying modern technology underscore the serious side of a subject with which the author makes such good sport. A great distraction for math mavens at any knowledge level. --Gilbert Taylor
conversations.from: human
conversations.value: Give me the first five paragraphs for this book.
conversations.from: assistant
conversations.value: Professor Stewart's Hoard of Mathematical Treasures
  Abbott hit on a cunning way to get his fellow Victorians to accept the possibility of a Fourth Dimension, by quietly pursuing an analogy in which 2D creatures living in a 2D world found the very idea of 3D space inconceivable, indeed heretical - and only then springing 4D on his readers, when he had softened them up. His hero, the modestly named A. Square, lives a humdrum life with his linear wife and polygonal children in a pentagonal house in the 2D universe of Flatland, which is a Euclidean plane. Abbott wove in some biting satire about the suppression of women and the poor in Victorian society, as well. And a few quotations from Shakespeare, and some allusions to Aristotle.
  Anyway, A. Square lives in a 2D universe and can conceive of no other. That is how things are, that is how things have always been, and that is how things always will be. And in any case, the Third Dimension is religious heresy and the priesthood of Circles will make short shrift of anyone who dares to mention it. And so A. Square continues his humdrum life, until one day he undergoes an epiphany, and becomes totally converted to the notion of a 3D world. This change of heart is triggered by a visitation from... the Sphere.
  Now, the limitations of his 2D nature prevent him from seeing the Sphere as a single object. Instead, he sees the circles in which it meets his flat world. A dot materialises into thin air in an empty room. Then it grows to a circle, expands to a larger circle, then shrinks back to a dot and vanishes. (You see why Victorian ghostbusters liked the idea of 4D.) He thinks the Sphere is some sort of priest, but one capable of changing its size. We Spacelanders have the luxury of visualising the geometry: a Sphere of fixed size passes through the Flatland plane, and the intersection changes as it does so.
  Now, says Abbott - though not in these words - a Victorian Spacelander, trying to contemplate the Fourth Dimension, is in the same position as A. Square trying to contemplate the Third. Protestations about the natural order, or the alleged impossibility of extra dimensions, carry no more weight in Spaceland than they do in Flatland. Abbott confines his mathematical discussion to enumerating the edges and vertices of a cube, and a 4D hypercube, but the point comes over quite strongly.
  By analogy, if we Spacelanders met a Hypersphere from the Fourth Dimension, we would perceive only the sequence of spheres that arises when it meets our 3D space. Like A. Square, we see a dot, materialising into thin air in an empty room. Then it grows to a sphere, expands to a larger sphere, then shrinks back to a dot and vanishes. (You see even more clearly why Victorian ghostbusters liked the idea of 4D.)
conversations.from: human
conversations.value: Give me three more paragraphs.
conversations.from: assistant
conversations.value: First, observe that the states in which some jug is either full or empty - which are the states allowed by the moves - are precisely those on the boundary of the picture.
  The allowable moves, starting from some state (necessarily on the boundary) amount to moving along a line until you next hit the boundary. If you start at a corner, and move along the boundary (say from 008 to 053), then you can't stop part way along, but have to go all the way to the next corner.
  So we can solve the puzzle by starting from 008 (lower left corner) and bouncing around the parallelogram like a billiard ball. The arrowed path shows what happens: we visit the states
conversations.from: human
conversations.value: Give me the last three paragraphs.. Start with the sentence 'To play the game you will need to make a set of cards - I don't know anywhere that sells them'.
conversations.from: assistant
conversations.value: To play the game you will need to make a set of cards - I don't know anywhere that sells them. It's worth the effort.
  He also sees the circles 'edge on'. Just as we see only a 2D projection - or a stereo pair of projections - of a 3D object.
  I made this up, but it wouldn't surprise me to find it's been used for centuries in parts of Lincolnshire.