But to walk the routeshown,you wouldhaveto walk throughbuildings!As that isn’t possible,you will have
to walk on streets,workingyour way over to the othercorner. This routewill be longer, but sincewalking
througha buildingis not an option,it is the only choice.
Our everydayworldis not a perfectplanelike the -coordinategrid, so we havedevelopedlanguageto
describethe differencebetweenan idealworld(like the -plane)and our real world.For example,the
directline betweentwo pointsis oftenreferredto by the phrase“as the crowflies,”talkingaboutif you could
fly from one pointto anotherregardlessof whateverobstacleslay in the path.Whenreferringto the real-
worldapplicationof walkingdowndifferentstreets,mathematiciansrefer to taxicabgeometry. In otherwords,
taxicabgeometryrepresentsthe path that a taxi driverwouldhaveto take to get from one pointto another.
This languagewill help you understandwhenyou shoulduse the theoreticalgeometrythat you havebeen
practicingand whento use taxicabgeometry.
TaxicabDistance
Now that you understandthe basicconceptsthat separatetaxicabgeometryfrom Euclideangeometry, you
can applythemto manydifferenttypesof problems.It may seemdauntingto find the correctpath when
thereare manyoptionson a map,but it is interestingto see how their distancesrelate.Examinethe diagram
below.