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95 There Is No Vocabulary—Well, Almost Nonetheless, the shapes are either four triangles or two squares. Each count is fine separately. All of the sides of the triangles and all of the sides of the squares are free. Only the sum of the triangles includes the squares, and vice versa. And these aren’t isolated examples that are safely ignored. It’s also the same for the shape in four different ways with two polygons, when three concave polygons, a trapezoid, and a pentagon are added to my vocabulary And possibilities grow exponentially for a vocabulary of polygons
96 I What Makes It Visual? and corresponding triangles in the shapes in this array It’s also good fun to play around with squares and grids—this reminds me of ten-bars— Everyone agrees that the shape is four squares But I can also make it with three squares. The two interior squares may be on the left diagonal or on the right one
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SHAPE
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( 2006 Massachusetts Institute of T
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Contents Acknowledgments ix INTRODU
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INTRODUCTION: TELL ME ALL ABOUT IT
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3 Answer Number One—What Do You S
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9 Answer Number Two—Three More Wa
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11 Answer Number Two—Three More W
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33 Trying to Be Clear Points aren
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35 Trying to Be Clear and twenty-fo
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37 Trying to Be Clear things look.
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39 Trying to Be Clear on correspond
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41 Tables, Teacher’s Desks, and R
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43 Tables, Teacher’s Desks, and R
Page 56 and 57: 45 It Always Pays to Look Again In
Page 58 and 59: 47 Background always more when you
Page 60 and 61: 49 Background Getting it first and
Page 62 and 63: 51 Background and not These are the
Page 64 and 65: 53 Background and count as I please
Page 66 and 67: 55 Background and time. The way Eul
Page 68 and 69: 57 Background them apart—a triang
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Page 73 and 74: 62 I What Makes It Visual? (2) What
Page 75 and 76: 64 I What Makes It Visual? Whenever
Page 77 and 78: 66 I What Makes It Visual? calculat
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Page 81 and 82: 70 I What Makes It Visual? more tha
Page 83 and 84: 72 I What Makes It Visual? Table 1
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Page 89 and 90: 78 I What Makes It Visual? formula
Page 91 and 92: 80 I What Makes It Visual? But what
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Page 97 and 98: 86 I What Makes It Visual? I see a
Page 99 and 100: 88 I What Makes It Visual? But this
Page 101 and 102: 90 I What Makes It Visual? contains
Page 103 and 104: 92 I What Makes It Visual? and othe
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Page 111 and 112: 100 I What Makes It Visual? and the
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Page 115 and 116: 104 I What Makes It Visual? to the
Page 117 and 118: 106 I What Makes It Visual? Table 2
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Page 121 and 122: 110 I What Makes It Visual? artifac
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Page 137 and 138: 126 I What Makes It Visual? What Sc
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Page 141 and 142: 130 I What Makes It Visual? be desc
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Page 145 and 146: 134 I What Makes It Visual? forget
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Page 149 and 150: 138 I What Makes It Visual? Why is
Page 151 and 152: 140 I What Makes It Visual? see wha
Page 153 and 154: 142 I What Makes It Visual? to calc
Page 155 and 156: 144 I What Makes It Visual? How cav
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146 I What Makes It Visual? togethe
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148 I What Makes It Visual? and six
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150 I What Makes It Visual? and its
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152 I What Makes It Visual? these h
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154 I What Makes It Visual? So how
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156 I What Makes It Visual? (TRI(XY
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158 I What Makes It Visual? The fir
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160 II Seeing How It Works was thre
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162 II Seeing How It Works and lowe
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164 II Seeing How It Works Back to
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166 II Seeing How It Works Divide e
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168 II Seeing How It Works There ar
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170 II Seeing How It Works while th
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172 II Seeing How It Works there ar
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174 II Seeing How It Works This has
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176 II Seeing How It Works And noti
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178 II Seeing How It Works looks ex
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180 II Seeing How It Works meaning.
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182 II Seeing How It Works and the
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184 II Seeing How It Works Embeddin
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186 II Seeing How It Works both of
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188 II Seeing How It Works but in a
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190 II Seeing How It Works It’s e
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192 II Seeing How It Works of one i
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194 II Seeing How It Works how it w
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196 II Seeing How It Works Table 7
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198 II Seeing How It Works of these
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200 II Seeing How It Works maximal
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202 II Seeing How It Works They’r
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204 II Seeing How It Works So, bðA
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206 II Seeing How It Works made up
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208 II Seeing How It Works boundary
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210 II Seeing How It Works First, t
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212 II Seeing How It Works topology
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214 II Seeing How It Works This has
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216 II Seeing How It Works where po
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218 II Seeing How It Works Operatio
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220 II Seeing How It Works is part
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222 II Seeing How It Works In parti
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224 II Seeing How It Works suggest
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226 II Seeing How It Works intricat
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228 II Seeing How It Works see what
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230 II Seeing How It Works to show
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232 II Seeing How It Works It’s a
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234 II Seeing How It Works that can
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236 II Seeing How It Works But supp
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238 II Seeing How It Works And toge
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240 II Seeing How It Works with poi
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242 II Seeing How It Works It’s f
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244 II Seeing How It Works to limit
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246 II Seeing How It Works and two
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248 II Seeing How It Works And the
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250 II Seeing How It Works (inducti
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252 II Seeing How It Works Two seco
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254 II Seeing How It Works Or I can
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256 II Seeing How It Works I can’
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258 II Seeing How It Works —and s
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260 II Seeing How It Works Now, no
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262 II Seeing How It Works up of se
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264 II Seeing How It Works These co
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266 II Seeing How It Works Why? The
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268 II Seeing How It Works and its
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270 II Seeing How It Works square f
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272 II Seeing How It Works descript
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274 II Seeing How It Works produce
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276 II Seeing How It Works points.
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278 II Seeing How It Works x fi y t
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280 II Seeing How It Works Indeterm
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282 II Seeing How It Works Or I can
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284 II Seeing How It Works applies
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286 II Seeing How It Works the same
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288 II Seeing How It Works in terms
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290 II Seeing How It Works It’s e
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292 II Seeing How It Works If a rul
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294 II Seeing How It Works But then
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296 II Seeing How It Works And, cer
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298 II Seeing How It Works are all
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300 II Seeing How It Works combine
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302 II Seeing How It Works In fact,
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304 II Seeing How It Works next pap
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306 II Seeing How It Works Table 12
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308 II Seeing How It Works initial
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310 II Seeing How It Works Kinemati
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312 III Using It to Design (3) desi
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314 III Using It to Design does mor
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316 III Using It to Design that I d
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318 III Using It to Design don’t
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320 III Using It to Design fix the
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322 III Using It to Design Figure 1
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324 III Using It to Design —divid
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326 III Using It to Design Perhaps
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328 III Using It to Design I seem t
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332 III Using It to Design Then the
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334 III Using It to Design and ‘
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338 III Using It to Design But this
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340 III Using It to Design but occa
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342 III Using It to Design numbers
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344 III Using It to Design to start
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346 III Using It to Design The rule
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348 III Using It to Design Everythi
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352 III Using It to Design Let’s
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354 III Using It to Design ever hav
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356 III Using It to Design (2) Furt
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358 III Using It to Design that wor
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360 III Using It to Design with the
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362 III Using It to Design are equi
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364 III Using It to Design and in f
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366 III Using It to Design to the p
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368 III Using It to Design rules th
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370 III Using It to Design x fi bð
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372 III Using It to Design These we
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374 III Using It to Design easy to
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376 III Using It to Design and spir
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378 III Using It to Design I said I
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380 III Using It to Design include
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382 III Using It to Design x fi x i
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384 III Using It to Design It’s g
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386 III Using It to Design take car
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388 III Using It to Design wealth o
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Notes Introduction 1. S. Pinker, Th
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393 Notes to pp. 48-50 Langer’s d
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395 Notes to pp. 51-55 19. H. L. Dr
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397 Notes to p. 156 9. C. Alexander
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399 Notes to p. 304 of lowest-level
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401 Notes to p. 305 24. The ‘‘n
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403 Notes to pp. 306-387 35. G. Sti
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405 Notes to pp. 388-389 M. A. Bode
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407 Notes to p. 389 The essence in
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410 Index Aristotle, 81, 167, 337 A
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412 Index creativity and (cont.) re
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414 Index greatest lower bound, 224
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416 Index maximal elements and basi
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418 Index Quine, W. V., 57, 58, 210
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420 Index shape grammars (cont.) an
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422 Index Van Gogh, V., 403n1 Vanto
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