# Geometry, List 3

December 1, 2022
Review these terms and concepts related to geometry that may be tested on the Quantitative Reasoning section of the GRE test.   altitude
We were flying at an altitude of 200 miles above a sphere whose radius is 4,000 miles.
asymptote
The curve tends toward positive or negative infinity, always approaching the asymptote but never reaching it.
circumscribe
Roughly speaking, he started out by considering the ratio of the areas of a circle and a square that circumscribes it—which turns out to be π/4—she explains.
complementary
“Here we go,” Princeton says, as they begin a lesson on such concepts as parallel lines and complementary angles in the quiet coziness of the family’s suburban home ...
congruent
We learn how to prove that lines are parallel, or shapes are congruent or similar.
dimension
The physicists also knew that there were already three numbers associated with the electron, which corresponded to the three dimensions of space it could move in.
equidistant
Having to decide slowed the volunteers’ reaction times by about 30 milliseconds, especially when the target was about equidistant from both hands.
hyperbola
The distinction is that the hyperbola is defined in terms of the difference of two distances, whereas the ellipse is defined in terms of the sum of two distances.
hypotenuse
Understanding all the relationships between different trig functions and different types of angles is vastly simplified by setting the hypotenuse of all the right triangles equal to 1 and placing them inside a circle.
inscribe
Now imagine trying to estimate the size of the triangle by inscribing little rectangles inside the triangle.
perimeter
Containment usually describes the percentage of the blaze surrounded by a fire line – a perimeter around the fire that’s been dug down to mineral soil, leaving no fuel to carry the fire across the line.
pi
Critical mathematical applications such as Fourier transforms, Riemann zeta functions, Gaussian distributions, roots of unity, integrating over polar coordinates and pretty much anything involving trigonometry employs pi.
postulate
Euclid begins with 23 definitions, 5 axioms, and 5 postulates and derives all sorts of theorems from them.
A gently surrealistic depiction of a suit jacket made of neckties is literally split among four canvases, but more typically the Peruvian artist uses quadrilateral shapes to divide a single-panel scene.
scalene
For just 110 rupees, I received a giant scalene triangle of thin, buttery dosa folded around a creamy mixture of potato dotted with mustard seeds.
similar
The AdS theory describing the same objects in the presence of gravity showed similar symmetries.
symmetrical
Because it’s easier to encode instructions for building simple, symmetrical structures, nature winds up with a disproportionate number of these simpler instruction sets to choose from when it comes to natural selection.
theorem
Its fundamental theorem tells us that any mathematical object, no matter how complex, is entirely determined by its relationships to similar objects.
transverse
This is sometimes called a cross section, and, if the transverse cut is at an angle, it is called an oblique plane.
vertex
Each interior angle of a regular heptagon is a bit over 128 degrees, so when we put three of them together at a vertex, we get more than 360 degrees.

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