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Pages 183-218

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From page 183...
... ~ changing u:nive~e ~ our best a~:~The most emotive medium ~r pedo~ing these tasks is mathematics. With ma~atics ~ build maim unifies and take them apart to see how It tick., ~t Piggy twit )
From page 184...
... 184 4~:~Y in "tech;~ol~ tmns:~- p~s pewei~d in ~ single =~mple ~ -~e Pi aCmss the entire sw~m -of sclen~e an~d Ad ~E ~[:E~CS OF CI=E The Id ~~h ~ ~e m~m of cha~ c~ be ~~d up in ::: ~~* m^~ In :~: ~e ch~ mtem Is mo eled all: ~ ~~al equatI~ (~' ~ ~k equation)
From page 186...
... As the twent:~ centu~: ~~ to ~ closet ~ ~~ ~~t ~ = iCs is I ~~le—ose Id :s vanish. Mathem~i~ ~ ~ ce ~m ~ d - cooping in d.0= my.
From page 187...
... M~nv ma* ~atical concepts can be gmsped we: be:~g exposed ~ their Army Amp Using ~ :~ea :s gu:te died mom dwelop-~ng :~- Tt :~s po-~le to "~- qu:te a~d =~s to oh: by :~s of exa*
From page 188...
... ~ ngomus pmof ball ~e ~-~ Aim- ~~- -- ~.~ :n ~e ~~r th~ =~.~r expen~ S~ 15 :~m o~y ~~d the~ =~.~..~f ~ ~~ perwn, ~t has- n~ ~ been—hem ~ pi mans and = an acts pmbl~ ~r Fad re~. The ~ ~ V16~t and mn~ Of ~s ~~ ~ m - ~s m~cs win be unposed not ]
From page 189...
... :~ Eli ~~ t5~ ~~ ~= It 0[ I, Ire 4;0 i~ t~ a~i=~-~.
From page 190...
... ~1 description of 1be mast Mob cut sbo~s a population tab increases may al bra bul lben ex~ne~iaDy. Tba1 is, 1be breeding population increases by a
From page 191...
... Odor children can ~ set mow ambitious tasks. the water l - ~l :n ~ p0~$ t350 ~~: 0t i:~5 0~ ~ bush' the :movements of the stock market' cxper::~ts Am ph>Ys:cs and chem:~oY iaboratones.
From page 192...
... Spasms and Nebulas lo gene~le 1beo~lichl data, lo look far ~pal~=s, and 10 sampan 1beo~ mild ~11~. D~_~ Stems Ibe neat level of explosion is to Angel not Be pa1~1e~s in 1be numb beg but Be ~ 1ba1 Ages dab 10 these pallerns In 1be traditional
From page 193...
... Ibe populalionleveI ) = ~/~ is a ~o~leveI: once il is abed Abe new huge, ~+1~> is O$ es are aD subsequent valuer To Judy bob population compacts Bulb 1be cull level, ~~ can expr ass ~~)
From page 194...
... d'h~wA~~= ~ : (~67 t56~0 '5 ~~ ~ en=ps~e the ms-~:;:~s in ~ sinde Mimetic ~~t ~h as ~ t~e serum By: ~ ~ ilk ~ I: :~S ~~n 1~ ~m pnncI:~- art: ~~s ohe~n ~e ~~e tha~ mnt~s Ohs (~. -I W~ 1~ =n be in~=d and stu~ ~m—IBM of—tues ~ mon as in beam their ~~ of Bigamy Guam 0r y~ balm thev =e ~~ ~ =~- However ~ :s also Cam to derive th~e ed ~e~ ~~e Radiate ~~s, =6 the1: t~nt N-~er~ ~enmen~ The ~~In :~w nisi an ex=~;~nt ~~tv for numeral ex~ pen~s u~g oni~ elemen~ anthm.~tic ~ =~- Ewn elementa—Y schoo!
From page 195...
... ~e main - ~~l e~t is ~ o:~:~n with ~ penod Of ~~t SS d - - How - ~~, as the t~ series sho~' the ~ i:; Bill the ~~:~ thin Chat :s decimal mmplex. Ma~ of the peaks in the gray aw do~, ~~:~ mom Misshaped than ~~S689064 ~0 height of the pe ~ OrC~0 SO'~ N~ Aft: : A: :~} $# 00 200 300: 46~ 500 ~O 700: ~ ~ ~ ~ :?
From page 196...
... ~ O{~ ~~ O5~6 -I dw to the wpuladon iambi of—~t n:~- ~~:rs m~ due to out~ :~s wch ~ ~~d ~, ~~, :~r ~~:~e ~ the Eli ~ of Ma~ :~n ~ sky. How ~ ~ we tell - :ich am - .~9 T:t would be =~y to assume that ~~e ~~:~e I: p6~$ the ~~n in - ~r size—=e ~:~d to outs:~ ~~s but th~ ~ ~ ~ i.~sin~ A. a0 ~ ~ ~ ~ dw ~ ts due to Som ~2 ~ l~ ~~g m:~h an In: c~e x' TV 0~~ this 855~;= bear 6 in Inexpen~ mth models simile ~ the w i~ show that s~-e math :~ can.
From page 197...
... * -I Ve~:~t I~ is absent from its continuous analogs - itch vie:~s only ~ smooth Stashed curvy.
From page 198...
... Children as young as ~ ~ or ~ ~ =:n use ~~e packages- to experiment ~th the bob~ ior of the =~ar elliptical emits f ~~-~> sty ad the 00-~6 ~ bod:ics. :13y us:~g these p3~87 t~ 08~ g8~ =~0 idiot t~0 t56 ~ And?
From page 199...
... day Ace- ~~ ex - ~~* ~s should be =~ed out fin mathematics dass~ as ~D, ~ an integrated pa~ of the de~ elopment of imunion ~ ~~ and motmn ~ f b: Alit itv and chacs.
From page 200...
... BY Y Y l! {s periodic be cau~ chit same act:-~:~s are Domed -~-~:ir and -and against and :~t must bee stable s:~e ot:~ise it wYou~t BODY Juggling two bod:~s :s Am: ely simple, ju~ng more quickly becomes Ale compl:~ed 1f teaches children to ~ u~, theN will leam qu:ickI:V about the complexity 0f d>~i031 57~;~> Thwart ~~ 3~ ~6 th~ p6~0 p~tg>=i 0 juggling fir Why is j~i0~g 5~9 Want is th~ 3~ 0f Or ~cd:l5~:~:?
From page 201...
... T~' enters when this ~ - ~s m~e ~4 ~~:~e th~ the state of ~e svst~ is descnbed by the is of ~ ~~nt in s~e hid ~mens:~ =~' - :~h sc:~ti~s c~ ~~e spate- As the ~Y~-~m ~~' this pOl.~t win m - ~' tmci.~ out ~ cu - e in ~~e spa=+ Tn oiler ~r ~ system ~ retu:= t~o :ts :~;~! ~e, this cume mum cIose up i=O ~ IOOp (~,~;~C 6)
From page 202...
... ~e 00w ls typify tndic~ ~ =~ imes': = to ~ tl~me evolution of ~e coord=~es of VanOus :~al pO:~ts ( ~~e 73^ Arrows mark ~ d^~.-~n of mot:~-n Of time. Bed =~t of =~hi~ the ch=~s :~n a si~e wnable' they =n be ~~:~=d to- ~~se ~~.~ Tread of plmun ~ ~~ ~ ~ ~ ~ ~ ~~ ~~ A ~ Mar =O ~~ ~ - ~0 Of ~~S O~f WO ~~t I in WO coo~in~e Erects Such ex~eS \~ll dewIOp insight l~ ~e mul d~ ~~ of cha - .
From page 204...
... NeXt, computer mOdels of ~ ~ as t~e ~74 50t ~6 *
From page 205...
... ~ - USA* Remade mth Jupiter Avow perils =y b - ~s ~:n mch o~:~, Aim ~e kind of Rabid: ~~ sweeps t~m ~ to hi: at—rich r=~ce no longer O~$*
From page 206...
... :~t ~~d ~ haM ~ find a mom ~a~c cxa~e of the essential u:~:~W of the emit solar Korea or ~ Bier example of the I:~:~s of cha=~ ~~ ~~*
From page 207...
... ( ~ con^~ce of sm~! i:~ctions asymmetnc solut:~:~s wall e:~ - ~n in an idealized pe - -I ~vmmet:~c math matinal s~Y~:^ T:~' such ~ "~< 57510= i=~ 00~:~5 sYmmetn~ Can b~.
From page 208...
... Tbeonli~ grope Raceme gas Seal Unmet abou11be center line. ltyou bean to ~~1cbibc fee elashc>1h~ Item obeys C~ude~s principles and Sl~yS ~symmeldc; lbet is> 1be disk dam got agate {~= 13~.
From page 209...
... Fix me ~ a dial ~12 ~ntimc1e~ gum the crater of ~c disk, and ~1~ Me ad of tbc #~r ~ lo ma along the center line as goon, fir example, gaping it 10 a mail ~~ you an ma by band. They In use a~spdng lo hold ~ ~ uphill, Cob 1be lamer end Basin: on a male, 1ben add whirls lo the 10p add walch it sway or buckle They can Mae a abode- Tom a Deducible meld Hap, pu1 whirls on lop, Ed ~atcb ail collapse.
From page 210...
... Thissbo~sbo~ lbocondnuoustempo=1 ~ mew ofa Ready Baa backs lo ~~ lbe discrete symmetry of a periodic one. Symmel~ baaing is im~~anl in biology.
From page 211...
... 9-11 ~ ~ URE ~ 4, Cr=~n ~ nd deSt=~n of symmctm ln ~ he ~1 opmen t; ~ ~ ~ ~~g ~ ~ By ~ 6~D ~ ~ =~ - ~ ten tr~ ~ ~ a~ A ~ then bll~ <'
From page 212...
... W~ I: ~ N~y ~ c:~= ~~ Bog ~h o~y ~~= ~~- id ~~n ~ ~~ ~67 i0~ t0 ~~= ~~ I' M—e~:~1~, Me development of ~ c~ dent d~ gastmIa~ than lS ~~y a=~s ~ tbe Cut. -of ~ ~~ shell (:~w 11~.
From page 213...
... ~ ~ ~ /~ / 91 ~ OO(RE 15 ~ fig cb~ill. ~~n Ha i~ilily in one ~1~ ~ ~$; in (a}, ~in~ilily in Id di~on bang up ~ SO inn IS.
From page 214...
... 214 + HOL~RE 18. Coma models ~ Is on animal skins sb~ov Idling Cults.
From page 216...
... gut, Jogs D ^~ he 1 ~ i~ sag.- ~~ 2i8 gab, 19S~, ~ am halo ad River, ~ Hi.
From page 217...
... ACE: ~ Cad Pa Diva 7~ #~ ~~~ aim. aim, lo Enema ^~# 19$9, i#73.


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