Exam 11: Mathematics and the Arts

Solve. -Given 0.22 centimeters is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation $\varphi = 1.62$

Form a tiling from the given figure using translations and reflections. -

Provide an appropriate response. -Which item is not related to the golden ratio?

Provide an appropriate response. -The golden ratio divides a line into how many pieces?

Solve. -A line is subdivided according to the golden ratio, with the smaller piece having a length of 7 meters. What is the length of the entire line?

Provide an appropriate response. -Which subject was not a part of the quadrivium - the standard curriculum in medieval universities?

Provide an appropriate response. -Which of the following is not a type of symmetry?

Provide an appropriate response. -Starting at middle G with a frequency of 390 cps, find the frequency of the note 36 half-steps above middle G.

Provide an appropriate response. -Starting with a tone having a frequency of 154 cycles per second, find the frequency of the tone that is one octave higher.

Provide an appropriate response. -Starting with a tone having a frequency of 761 cycles per second, find the frequency of the tone that is three octaves higher.

Provide an appropriate response. -Starting with a tone having a frequency of 579 cycles per second, find the frequency of the tone that is two octaves higher.

Provide an appropriate response. -Draw an object with rotation symmetry.

Provide an appropriate response. -Draw two cubes, one with perspective and one without.

Provide an appropriate response. -Which regular polygon can be used to make a tiling?

Solve. -Given 5.1 kilometers is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation $\varphi = 1.62$

Identify all of the symmetries in the following figure. -

Form a tiling from the given figure using translations and reflections. -

Provide an appropriate response. -Starting at middle D with a frequency of 292 cps, find the frequency of the note five half-steps above middle D.

Provide an appropriate response. -Starting with a tone having a frequency of 159 cycles per second, find the frequency of the tone that is four octaves higher.

Provide an appropriate response. -The circle of fifths is generated by starting at a particular musical note and stepping upward by intervals of a fifth. By what factor does the frequency of a tone increase if it is raised by three fifths?