Geometry, List 2

December 1, 2022
Review these terms and concepts related to geometry that may be tested on the Quantitative Reasoning section of the GRE test.
The heat island effect is a phenomenon in which urban areas experience higher temperatures than the areas adjacent to them.
This led him to discover that the pendulum always took the same time to complete one swing, whether it was swinging over a short arc or a long arc.
Along those lines, if you bisect a person’s photograph and view each half independently, people usually think he “looks like” the left half more than the right half.
Observers at different latitudes see the star pass behind a different chord through the asteroid, so the observations can be combined to measure the latter’s size and shape.
To evenly heat the dough within, the oven is shaped like a cylinder with heaters lining every side; that way, the cookie is heated evenly all over.
Instead of its predicted path being a closed ellipse, its orbit was open, indicating that it would never return.
It is a variation of the basic principle that if you know one angle and one side of an equilateral or right-angled triangle, then you can determine the other angles and sides.
Water molecules have a particular bent shape that causes them to stack into clusters shaped like hexagons as they freeze.
The Lute of Pythagoras is based on the “golden” isosceles triangle, a triangle with two equal sides and an apex angle of 36 degrees.
It is also possible to pave the plane with infinite straight lines: just place them all side by side and parallel.
Think about it: a square or rectangle can easily be pressured into a parallelogram without changing the length of its sides.
Given that a smiley-face is 2D, presumably if it exploded such that its plane were perpendicular to the viewer, it would appear to look like a straight line.
The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon.
Geometric columns are seen in a variety of volcanic rocks across the Earth and are known to form as the rock cools and contracts, resulting in a regular array of polygonal prisms or columns.
The lack of interest was driven in part because John von Neumann, a highly regarded scientist, had in 1932 published a mathematical proof ruling out hidden-variable theories.
For 4,500 years, the pyramids of Giza have loomed over the western bank of the Nile River as a geometric mountain chain.
Often there will already be a cabinet offered as standard to fit into that uneven corner run, rhombus of a nook or sliver next to your stove.
Wherever that interior mesh mistakenly crosses over itself, the algorithm modifies that part of the contour, such as by untwisting it or adding finer line segments.
So a circle gets squashed into an ellipse, a rectangle turns into a trapezoid.
And the next thing I knew I was in a trigonometry class and they’re talking about sines and cosines without any mention that it had something to do with triangles.

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