Student facing
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finite figures, like the shapes we have
looked at in class, cannot have
translation symmetry. but with a pattern
that continues on forever, it is possible.
patterns like this one that have
translation symmetry in only one direction
are called frieze patterns.
expand image
1. what are the lines of symmetry for this pattern?
2. what angles of rotation produce symmetry for this pattern?
3. what translations produce symmetry for this pattern if we imagine it extending horizontally
forever?

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?