On the Shoulders of Giants New Approaches to Numeracy (1990) / Chapter Skim
Currently Skimming:
Shape
Shape
Pages 139-182
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 139... ...
in ~e s~n and n wo~, in a: ~~s =d video lmmS, in omamen~ design am ~ =i,—Or in tTi) ~C p81~' and in city abUity to Pi inte~' and create pattems is the kale to d~g wi~ the ~~d around us.
|
From page 140... ...
N~nheless' it is helpful to days each of these ~~:~.~N O~e of the =~t ach:~:~s of ancient mathematics was We d:is e~ that them are exs=~7 ~ (~x, thwe~imensionat 5689~5 ~80 5~5 8~6 00~ 0{ t6~{ p0~57 cite the same nu0~r of polygons meeting at each -my ¢~e shy known as Be rehear ~ ~ ~ ~ ~ ~7 ._ · ~ · ~ .
|
From page 141... ...
mare -A ~ Kit ~ :~ - ~ FIG:~E ~ ~e :~e =~r - ~~ mb Is =~ - of ~ sI~e ty~ of r - ~r =~ m~h the =me n~—of ^~;~s ~~ng at =ch comer. Th~ t~on' , and :~r<~n =e m~ ~ ~;~, ~~e cu~ :s made of -I a~ the .-~ Is made of wn~ mu~ ~ ~k X]
|
From page 142... ...
It is gag ~ think of other others 1h~ bee 1be same s~mcldes, or selLcon~en~s, as 1be Guam: Abe Rod Cross sy l, a braced ~i1b Cur buggy speed ~ads, ~ circle of Cur dancers and a Leaf clover (~i1bOU1 i1S stem) are a ~ examples.
|
From page 143... ...
~.~:= :c nwRE 3:.
|
From page 144... ...
/~ ldpolo~i ~ equi`~ienceiseven more genenElban combing narrow eq~uiv~ence.~F~om the ~andpOin1 of 10pOl~Ogy, allpolygonsare loopsand allconvex poRbedr~are Mike. Piggy a~guedlba110~polo~cal concepts occur pdor lo metric ones in child development; a Old gnat ~c~izz a low ~= disli~uisb.ing among kinds of loops, such as age.
|
From page 145... ...
Opus ~~ _~ he ~c~of~e~n, ibid lbe ~~= beech ~ ~1~~ ad ~ Pus Ed ~~ endue ad ale, ad abet cap of ~~: gab ^~^ adzes he JO divans ~ a -~~ ad ~ lass Anus zeal ~ gnu oaf. ~de~di~ cab chic ~~ y ~~ ~ Menu ad ~- as ~11 as Them ~ ~ .
|
From page 146... ...
146 ~WA~ go: ~Y Awake - ~- ~ =~e ~ sh~' we =e ~e "me dme Agog it y t.~e a~ (^C-~ g 1.~.
|
From page 147... ...
tat? nG:~S ~ FOur natum!
|
From page 148... ...
~ ~ Wan chi.~n m~e sh~= out ~ bloc~ or ~' th~ oDen imitate the d:~e com:~sit:~s ~ ~ see ~ar~:~em (Firm 91. Nature too creates patterns.
|
From page 149... ...
Stu~s q=~V hisser ~at ~~re are onIv ~ I- ~ ways to -do Whist delis ndamen~ pro=~y of Am can be studied ~ ma~ I~^ For ex ~~ it can be smdIed i: and "~ when the o~ts BAN ac~d · ~ ~ ~= ~ ~ tA quadniateMs' and hexagons Cadre iO)
|
From page 150... ...
Copters ~ ~ g0~tA3) a~ 3~A~A~ a plant mth =~ =~e ~d once w(~c 6t )
|
From page 151... ...
By doingsothoy gill babied animpoMenlk~sonin1be ~ dean Judy of e. ReOcctionsgen~e patterns Aid a hinge nu ^ cofsubunits: pad e~nstb~ have Own as Dallas Minor ~~nm~.
|
From page 152... ...
Ma Add. nOURE 13 ^ pyre case The line on 1be It'd aces indicts 1ba1 1bc c~l~'$ illegal Use lack ~~ of 1be symm~ ~ Be cur.
|
From page 153... ...
a: ~3 |
From page 154... ...
154 ~ ^ sit am: \ #)
|
From page 155... ...
SH:~^ WN - I::: ~41 :~= l6* CO:~x d~ - a~ f: O~ - m eg uDate~ ~ ~ r=~d w11b ~~.g ~ of ~ ~=,ls~ ~~ - ~ or' ~e ~ awes m~ be jorned ~ ~ beam =~ cOmer.
|
From page 156... ...
A one~imension6I is a ~1 of spiels equal spa glow ~ ~line. (~1bou~ ~ can dam ply pea of able set, ~ assume Abe ail ~ on amp.)
|
From page 158... ...
~ ~ ~ O ~ BOIL lo; to ~ ~~~ ~~S from ~ si~e =~! t:~- in the earIv st - s of =~ divided :~to =~- =~:is that ~ a~d divided again- ~e sPtud>Y of how dividing cells organize t:~s into tiss:~s a~d then Into organS :s
|
From page 159... ...
may baa no lattice slipup Such tibias a~ of Hal inle~sl leeway ~~ 1bey spa mop S1~C progenies Fib amp neat diamond Caroline malehal$.
|
From page 160... ...
~~~ tetrahedron :s ~ wmb`natartal ner w~ - or all: simile wamnIng sho~ that there ar~ two com Nimbi types of pent~, -~m with :~e ~~s (~u ~ 5~d them i:n Flare 6) K ~~= 870 0~ $~en Wpes of he- (~m 2 1 5' :: of :~e ~ cube d:~:r - v there are no mo*
|
From page 161... ...
w~ Of ~e ~~= of ~~ plus the =~r of ~~s :s equal to ~e n;~= of e~s plus two ~~s c~ be ~~n s~y Fat ~ ~ ;~2 whem ~ :s ~e number of ~= (~r cam) -of the ~7 ~ is t~ ~~ 0{ - It 8~6 ~ is t56 ~~: 0t 66~- (~t i~ 08~ t~ ~~ -I equation Pith she n-~3ks :n F:~ms -l, 6, l-9, ;- 27)
|
From page 162... ...
INS -ah Cat ~ $ _ \ .~ ~ \_ cy =~ _~#~# ~ ~ -~ $~ _ _~ ^~-_~ __~_ 1/ ~ ~_~ ~ ~ ~_ _ .
|
From page 163... ...
Anions of we earth qude why Am pm of the sur~ of ~ sphenca1 JO =n be closel-~ ~~oximMed b~ ~ ~~:~- Bm the rep=~n ~s ~~ and wo=e ~ ~~ ~ ~o Ike the ar~ =~ - b~ ~ m~^ The =~ti~ - ~~n Awes arid 0~ ~s :leadis ~~y to w~ ~Ma~ne~l—~~ que~io:~. You can,: Mae ~ sphere b~ ~~g up ~ same of p~ so to ~~e 0~ ~~, ~u :: to- p~t ~e hose in s~e ~.
|
From page 164... ...
== ) n dl~= ~~ =e :^t ~~r is And promo Fir 0~7 ~ ~ 00~10 =~5 cam as prom shadows of ~ ~~e ~(Fi~ 233~M ~ more advanced :~ ~ -in the of shows ~ m~s in wake onTy ~ oWIme of the map ls retains..
|
From page 165... ...
~ &~ FI0URE ) $ Tne 1~} loges of the MathematlCal Ass=~-~:n of Am¢~ :he old one 15 ~y OX Lhe new one ts accur=e Th~ error ~d detecLIon ~r mam, ~; ~ ,~ >~ ~ ~ ¢]
|
From page 166... ...
Mar Guam, ma, Holland. ~ -~ ~~ ^ Lee ~ons~bon lf lhe ~iSl,S problem is lo ~p=~nl a 1b~e~ension~ sb~ on O~ so 1be views problem is 10 Size -~ shape the imp is supposed lo ~1.
|
From page 167... ...
~,.g t~ ~;5 3~.6 I;, ~0 5~,5 i~tr0~$~t 7,0. the stud~ of ~Yh2~" ~00 ~8= i;: thus te invaluable in the stud> of shape am should ~ 0,5~d wYhe:n appropnate" .~:~, Aft ~n SHOUT know so:~ng of the geo-~~ ~at undedics computer Chick al:!
|
From page 168... ...
As incrm~ngl:y deta~ Wages of ~ w~ }A ~e Act sm~~ am ~e Army hidden alit ma~ vI~le ~ m~ techn~y~ e :~d to understand his bm~d Arced of m~g ~~= ~ ~~ ~~. M=~ng :s ~ m~or Verne of co~ :;~emancs bec=~ :t pride ~ =~l =d icing wad ~ Amaze r - ~~s amo sh~s =d panes -I very ~~ ones)
|
From page 169... ...
- ~~ ~r soh,:~g t~ nddIe of the moods `~nge 5~.7 I+~ ~ x ~ he bm—t to hIs teles=pe ~ Spec:~—holder~s share, (~s S.~- Govern would 53~7 that is, ~ OVCSi=t 86~6 ~ EXAM unsmooth sphere of the moon :~:~d bsY ~e 3~75 :~k:~ i]
|
From page 170... ...
xnsla~ imp an :im~- wn:~es Ham Canaan wn Band ail ~ remet we of ~e Sd=~ ~ - n B-~r ~~s on to ~~* .t out that thIs tmnd~n must be done bY the educated ~ as well as by the i:~:~er~ wo~gs of the computer.
|
From page 171... ...
~ti:~g a~ and sciences We =n at50 :~0 tt:0 ~- 5~ of our Demo technolo~- The p:~cipl-~s off the electmn micro sc~' the md:io telescope, and ultrasOund am :~ot wholb~ beyond the sc~ of the WI: cumculum, him school students can' if ace wash, Ie~ the fin neceSsa~,,,~ tO u.~.~:~d the action of these and other :~= imaged techniques. Indeed ~ ~~s on Shape makes manly aspects of modem technology :~h more accessible than :s co:mmontv s:~- Here are just three :::
|
From page 172... ...
. amp I Ed n Bait ~~ ~1 quad Ed fits ^e~ Di$~i=:; ^~^ awls Glut =~$ Guitar ~1~= act Al Tiling tbc ~~ fit ~ Is ~~1 Aims Same ~ ~ Nazis Cadge; =~n Gamete Elms Is e ~ bite ~s~^ Id of ~~ and ED ma; Amp tb~ _ ~ ~ I DO Ian a~ using simply mans Ski Clef ~= and 1~1 cut I atoms ~ 3~0 -~u~ ^o ~~ ~1~ of 1~ abut; potions; mat land iamb ala; ~im~~ibl: h admit tiv~d~ ~cb~i=1 doing; ^ ~ 1c ~~ Talent a~ micmsco~ Has mat; tbc ~~m Bang I ED card Tuna ~~1~ Gaping On ~~ 1bc Cog Spurn Aphid Spur P1GLRE 30.
|
From page 173... ...
5~ ~~pg¢~:,g,:~r tt~ {gg¢~;~h0~3, 0~57 8~0 0~:~=i~" ~6il6~ 0~ ten ieam to make paper snowpakes in s-~^ an cX0'rClse that =n easllv
|
From page 174... ...
as we hew seen, ~s an Pain of the ponc~;~es of mirror ~* These same refl~:n p:~:~$ un~:~d mntem~:~ te¢h;~*
|
From page 175... ...
The contin:ui:~g debate indicates ~~t :~e of ~~e goals is pameulad wed ~d tn the ~~em situation.
|
From page 176... ...
5 of de~s ~d a~mph=s and: veer carafe jar. In o~r to a~ze shapes, ~ud¢~ mu~ key bow Ibex lengths, ~~' a~ - ~~= ~ w~ a~ Shear and ~~ - As*
|
From page 177... ...
mo~v to the It that Wave discipline boMem h^e * not owes been*
|
From page 178... ...
:~n expenmentatio~n is essent:~+ F6r - ampler when we ma Abe m:th our own bands~ ~ ~:n much more Tonsil I- :ts metric, =~bi:~nal, =d ~abi:litv properties than if we jug :~k ~ one. {if ::~d of ca - card ~~s we :~ t~e Me few plastic I, ~~k in b~Is of putty ~ in ma:~:mal:~ the c~e will wobble.
|
From page 179... ...
do. In teaching shape~ espec:~y in ~ workshop Attic ~ teacher :s unlikely to encoun~r ~e balk (~: mot1~\'ation or \be resides= that Aims 8~0 ~~.~ gamy I- #I ~0 t~ 8~t it ~ educatlonal cimies One emotive ~ to anew er questions ~~t the ~iUC3tiO~ \~ue of =~ng ~~pe Is tO hold an open house in ~ ~ ~;~ ~ ~~ ~~ t~t I 03;~ 5000~0 Aide 6~;5 ~ gaging invoiced w:~h the :matenal t50~5431~rC5.
|
From page 180... ...
Hey no flower ~1 ~ ~^ loam E Ads; in_> gay me paper ~~ me Nils in Acing me Flies of bang. abed Abed ~ ^~ Bus haul nag ~~ ~1~bi~ Blab lbe~ USA and Me nag Pep ~~- ~ be en~u_d by it cupola gal Eva s^plo~lio~n of shape ~~u~u1 1be enlist Rectum.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.