For furtherreading:On Beingthe RightSize, by J. B. S. Haldane,also availableat http://irl.cs.ucla.edu/pa-
pers/right-size.html.
LessonSummary
In his lessonwe focusedon one mainpoint:The areasof similarpolygonshavea ratio that is thesquare
of the scalefactor. We also usedideasaboutsimilarfiguresto analyzescaledrawingsand scalemodels,
whichare actuallysimilarrepresentationsof actualobjects.
Pointsto Consider
You havenow learnedquitea bit aboutthe lengthsof sidesand areasof polygons.Nextwe’ll buildon
knowledgeaboutpolygonsto cometo a conclusionaboutthe “perimeter”of the “ultimatepolygon,”which
is the circle.
Supposewe constructedregularpolygonsthat are all inscribedin the samecircle.
- Thinkaboutpolygonsthat havemoreand moresides.
- How wouldthe perimeterof the polygonschangeas the numberof sidesincreases?
The answersto thesequestionswill lead us to an understandingof the formulafor the circumference
(perimeter)of a circle.
LessonExercises
The figurebelowis madefrom smallcongruentequilateraltriangles.
congruentsmalltrianglesfit togetherto makea bigger, similartriangle.- Whatis the scalefactorof the largeand smalltriangles?
- If the area of the largetriangleis squareunits,whatis the area of a smalltriangle?
The smallestsquaresin the diagrambeloware congruent.
- Whatis the scalefactorof the shadedsquareand the largestsquare?
- If the area of the shadedsquareis squareunits,whatis the area of he largestsquare?