Geometry: An Interactive Journey to Mastery

2. :HKDYHFRSLHVRIWKHHQWLUH¿JXUHHDFKDW^13 the scale. Thus,
   201 ˜original size = ©¹§· ̈ ̧^13 d˜ original size,
   giving 3d = 20. This yields d |


3. 0.1111!""     0.1 0.01 0.001 0.0001 10 11 1 1 1023410 10 91.


4. We start with 1 equilateral triangle and add to it 3 triangles at^13 the scale, then 12 triangles at^19 the scale,
   then 48 at ^1 the scale, and so on.
   :LWKHDFKLWHUDWLRQWKHQXPEHURIWULDQJOHVDGGHGLVWLPHVWKHQXPEHURIWULDQJOHVDGGHGLQWKHSUHYLRXV
   iteration, and these triangles are each^13 WKHSUHYLRXVVFDOHͼ௘6HHFigure S.31.1௘ͽ

%HFDXVHDUHDVFDOHVE\k^2 WKHWRWDODUHDRI.RFK¶VVQRZÀDNHLV

22 2

24 6 2

12 3 2

2 2

1 3 11 11 12 1 48 1

13 11 133 3 134 134 1

13 11 199 9 134 134 1

134 411 139 9^19

(^111433)

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 ˜ ˜  ˜ §· ̈ ̧§· §· ̈ ̧ ̈ ̧

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(^42).

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Figure S.31.1