CK12 - Geometry

Numberof sidesof polygon Perimeterof polygon

3.141

As the numberof sidesof the inscribedregularpolygonincreases,the perimeterseemsto approacha “limit.”

This limit,whichis thecircumferenceof the circle,is approximately. This is the famousand well-

knownnumber. is an endlesslynon-repeatingdecimalnumber. We oftenuse as a value
for in calculations,but this is only an approximation.

Conclusion:The circumferenceof a circlewith diameter is.

For FurtherReading

Mathematicianshavecalculatedthe valueof to thousands,and evenmillions,of decimalplaces.You

mightenjoyfindingsomeof thesemegadecimalnumbers.Of course,all are approximatelyequalto.

The articleat the followingURL showsmorethan a milliondigitsof the decimalfor.

http://wiki.answers.com/Q/What_is_the_exact_value_for_Pi_at_this_moment

Tech Note- GeometrySoftware

You can use geometrysoftwareto continuemakingmoreregularpolygonsinscribed

in a circlewith diameter and findingtheir perimeters.

Can we extendthis idea to othercircles?First,recallthatall circlesare similarto eachother.(Thisis also
true for all equilateraltriangles,all squares,all regularpentagons,etc.)

Supposea circlehas a diameterof units.

• The scalefactorof this circleand the one in the diagramand tableabove,with diameter , is ,

, or just.

• You knowhow a scalefactoraffectslinearmeasures,whichincludeperimeterand circumference.If the

scalefactoris , then the perimeteris timesas much.

This meansthat if the circumferenceof a circlewith diameter is , then the circumferenceof a circle

with diameter is.