I'vebeenthinkingabouttheworldcoupleofBrady, andthen I wasremindedofthisreallyincrediblegoalthatjustturned a littlebitover 20 yearsoldonItwas a goalthatRobertoCarlosfromtheBrazilnationalteamscoredonFranceinpreparationfortheWorldCup 20 yearsago.
Oneofthemostincrediblegoalsinhistory.
Itwas a freekickthatdidn't seemlikeitwasverydangerous.
Hey, needstotake a shotfromreally, reallyfaraway.
Andhehadthisincredibleabilitywithfreekicks.
Wewentlikeitwasjustgoingwayoutofbounds.
AndthenthecurlofthelastmomentAndiwentinside.
Playerscanusuallydothiswiththeinsideofthefoot, buttodoitwiththeoutsideofthefootandhaveitcurledthatmuchissomethingthat I hadneverseenit.
I don't thinkanybodyelsehadbefore.
I do.
Yeah, we'regonnahavetoseeonthefifth.
Later, I waslookingatfootageandtherewereallthesearticlescelebrating a goalon.
AndwiththatinformationHowdowedeterminehowfartheballisfromtheMaybe I willtrytodraw a pictureoftheboxcandothisandupwiththepenaltykick I gotovertherealso.
Wecan't useitbecauseyousee, itisnotinthephoto, sowe'renotgonnabeabletouseitas a pointofreference.
Havingdrawnthedotwherethepenaltykickissteakandthere's also a littlearcrightherethatisactually a circlecenteredhere.
It's anarcof a circlecenterrightthere.
I don't evendothat.
Therewas a secondsentenceontheideaisthatwhenyoutakethepenaltykick, you'resupposedtobe 9 15 awayfromthefromwherethepenaltykickistakenandsothatplayerscannotstandinsidethatcirclesothatthey'rethatfarawayfromit.
And I thinkthatthefirstthingthat I wouldtrytodois I mightsay, OK, well, ifthisdistancerighthere, 16 and 1/2 andthenthisdistancerighthereiswhat I'm tryingtofindthis.
Callit X.
Ofcourse, if I know, extendthedistancefromthefromtheendingwillbeexplosivesteen 160.5.
Then I thinkonethingthatmightbeworthdoingisseeinghowthesedistancestransferredtothisredline.
Soifif I drawthislinerighthereonthislinerighthere, I feelliketheyshouldberelated.
Actually, 11 thingthatistrueisthat 16.5 dividedby X isequaltothisdistancedividedbythisdistance.
I thinkit's worthactuallydrawing a littlepictureheretokeepthatinmind, becausethat's goingtobeimportant.
Parallellineslikethisoneandthisone.
They'reparallel.
Andifwedrawtwolinesacrossthemlikethisone, thisone, thenif I measurethisdistance, let's say I callit a andassistancesbe.
Andif I measurethistoois a primeandAssistance D prime.
Andaslongastheselinesareparallel, so I'm goingtodropthisyeartosignifythatisanswerparallel.
Then I'm goingtogetthat a over B isequalto a primeoveryou.
Andsoitfeelslikeif I wanttofind X andthis, thenthen I mightbeabletorelateoverhere.
Andthegoodthingisthatthesedistances I cantrytomeasureinthispicture, So I'm goingtotrytodothat.
I'm goingtotrytosay, Okay, well, let's markthesepointsrighthereand I canactuallymeasurethesethings.
Sothenyoumightthinkthat 16.5 dividedby X sinceit's equaltothisdistancedividedbythisdistance, youmightthinkthatthatshouldbeequalto 4.5, dividedby 7.3.
Andthenyoucouldusethatequationtosolve X.
Exceptitdoesn't.
Andandwhydoesn't itmakesense?
Becausethere's a changeinperspectivebecausehereinthispicture, I'm lookingatthefieldfromontop, whereashere I'm lookingatitfromthefront.
Andwhen I dothat, if I lookatitinthisway, it's It's likewhenyouwhenyouwalkin a roomthathas a squaregridofftilesandtheonesthatareclosertoyoulookbiggerthantheonesthatarefartherthanfromyou, eventhoughthey'rethesamesize.
Andsowehavethesameissueherethatthispartoverhereactuallylooksbiggerthanitreallyis, andsoWhatweneedtofigureoutis, howdoes a changeofperspectivechangemeasurements?
And, uh, thisisaninterestingthingbecausethisis a very, veryclassicalproblemingeometry, anditwasfirstdevelopedwhenartistsandgeometriesweretryingtofigureouthowtodrawinperspective.
Andit's a littlepieceofgeometrythathasbeensomewhatforgotten.
Actually, I thinkweshouldtalkaboutit.
Wehave a greenlineontheredline, andthenthequestionis, if I'm standingrighthere, howdidHowdidthedistancesinthegreenlinetransfertothisisontheredline?
Soif I trytodrawpictureliketheonethat I drewbackhereexceptnowthelinesarenopaddle.
Theymadeit a point, thenthequestionis, howdoesthisdistanceandthisdistancerelate?
I wasteaching a classingeometryanditcametimetobeprojectedtoteachprojectivegeometry.
And I learnedaboutthecrossracialinthatclassthat I wasteachingforthefirsttime.
And I thought, Well, thishasactuallyreallypowerful.
I'vecometolovethecrossracial.
I thinkit's I thinkit's a beautifulthing.
And I thinkthere's thisreallyinterestingquotebyRobinHartshorn, whoisoneoftheworld's foremostkilometers, andhisdeckspokewhenhewastalkingabouttheclothes.
Rachel, hesays.
I mustsayfranklythat I cannotvisualizeacrossratiogeometricallyifyoulike.
Itismagic.
Youmightsayitis a triumphofalgebratoinventthisquantitythatturnsouttobesovaluableandcouldnotbeimaginedgeometrically, orifyouwere a geometryatheart, youmaysaythatitisaninventionofthedevilandhatedyourwholelifesodramatic.
No, I reallylikeit, and I thinkittellsthestoryofhowinmathematicsyoudon't gettochoosewhatfieldworkon, youknow, youthinkyou'redoinggeometry.
Allof a suddenthere's veryalgebraicquantitycomesinon.
We'reactuallyrelyingonthisprettydeposit.
Veryfactthatatleast I havenogeometricintuitionfor, and I thinkthat's reallybeautiful.
Plus, wehave a veryspecialtreatcominglaterthismonth, butmoreaboutthatinthenextfewweeks.
Butthat's nofun.
I mean, thewholepointofthisistobuystickersandtradedwithotherpeopleandsoon, andso I thinkweshouldgofor a littlebitof a morerealisticscenario.
I'vebeenthinkingabouttheworldcoupleofBrady, andthen I wasremindedofthisreallyincrediblegoalthatjustturned a littlebitover 20 yearsoldonItwas a goalthatRobertoCarlosfromtheBrazilnationalteamscoredonFranceinpreparationfortheWorldCup 20 yearsago.