Now let’s see how the SierpinskiTriangleis self-similar.
Lookat the trianglethat is outlinedin the diagramabove.Couldyou provethat the outlinedpatternis similar
to the patternof Level1? Becauseof this relationship,the SierpinskiTriangleis self-similar.
Tech Note- GeometrySoftwareUse geometrysoftwareto createthe next level,or levels,of the SierpinskiTriangle.LessonSummary
Fractalsand self-similarityare fairlyrecentdevelopmentsin geometry. The patternsare interestingon their
own,and they havebeenfoundto haveapplicationsin the studyof manynaturaland human-madefields.
Successivelevelsof a fractalpatternare all similarto the precedinglevels.
Pointsto Consider
You may wantto learnmoreaboutfractals.Use a searchengineto find informationaboutfractalson the
Internet.
LessonExercises
Use the CantorSet to answerquestions1-6.
- How manysegmentsare therein Level3?
- If the segmentin the Startlevel is unit long,how long is eachsegmentin Level2?
- How manysegmentsare therein Level4?
- How manysegmentsare therein Level10?
- How manysegmentsare therein Leveln?
- If the segmentin the Startlevel isSunitslong,how long is eachsegmentin Leveln?
Use the SierpinskiTriangleto answerquestions7-13.
- How manyunshadedtrianglesare therein Level2?
- How manyunshadedtrianglesare therein Level3?