Review Questions for Second Exam


Posted February 23, 2016

a) In addition to reflection symmetry, what other kinds of symmetry are there?
rotational, displacement, dilation

b) What are at least three examples of each of these kinds of symmetry, two biological examples and one example of a man-made structure?

c) How did Weyl define symmetry? (Something has symmetry, if there is something you can do to it (reflect it, rotate it, move it, magnify it) and...
it still looks the same afterward as it looked before.

d) A spiral snail shell has a combination of dilation (=magnification) symmetry plus what other symmetry?
rotational symmetry

e) An adult starfish has five planes of reflection symmetry?

d) A pluteus larva has two planes of reflection symmetry?

e) A sea urchin blastula has an infinite number of planes of reflection symmetry?

f) Therefore, some kind of symmetry breaking must occur around the time of gastrulation.

g) Does such an event create more symmetry?

h) Which is more difficult to accomplish?
To make something become more symmetrical?
To make something become less symmetrical?
To make something become less symmetrical, but not random?

i) Turing's mechanism is able to change symmetry in what way.

j) Therefore, Turing's mechanism is a way to break? or to increase? displacement symmetry?

k) Does Turing's mechanism increase or decrease displacement symmetry?

l) Therefore, Turing invented a contradiction = counter-example of Curie's Principle?

m) What changes in dilation and displacement symmetry occur during the formation of Liesegang rings?

n) When a donkey decides which of two equally distant piles of straw to eat first, it is breaking what symmetry?

o) When the higher-pressure chamber of the heart develops on the left side, what symmetry is that breaking?

p) Kartagener's Syndrome is a genetic inability to break what symmetry?

q) Is that a confirmation or a contradiction of Curie's Principle? Explain?

*r) Imagine that the differences between the left and right side of some kind of organism's body were somehow controlled by the stereo-asymmetry (stereoisomerism) of amino acids. Then would it be possible for a mutation to produce situs inversus?

s) What conclusion can we draw from the observation that half of people with Kartagener's Syndrome do NOT have situs inversus?

t) Flagellar basal bodies (axonemes) have nine fold rotational symmetry, but have no planes of reflection symmetry. What is the relation between this lack of reflection symmetry and the preceding four questions?

u) Please list at least five examples of embryonic processes that are mechanically analogous to the inflation of a water balloon?
(One example: expansion of the brain)

v) Before gastrulation begins, a teleost embryo has what combination of symmetry? During gastrulation, what symmetries do vertebrate embryos develop? Or break?

w) The curvature of a line is described as the rate of change of what? per distance along what?

x) A surface curvatures of what two shapes are the same in all directions?
Spheres & planes.

y) The surface curvature of a cylinder is zero in one pair of directions and some non-zero constant in the directions perpendicular to that.

z) The mathematical field called differential geometry defines shapes in terms of what properties?
NOT distances along x, y and z coordinates.







back to syllabus