Geometry, List 1

December 1, 2022
Review these terms and concepts related to geometry that may be tested on the Quantitative Reasoning section of the GRE test.
Heat those molecules and they reorient themselves ever so slightly—the right angles become acute or obtuse—such that the material contracts.
Because the planet is tilted at a 28-degree angle along its axis, it experiences four seasons, just like Earth.
Hardly anyone reckoned that struggling in high school to calculate the area of a triangle or the volume of a prism could be used one day to influence the outcome of an election.
This makes the average Mauna Loa eruption less explosive and contributes to the mountain’s long profile: about 10 miles from base to summit and covering 2,000 square miles.
To a topologist, three lines connected to make a triangle are the same as a hollow circle because one shape can be bent into the other.
Humans define π to be the ratio of a circle’s circumference to its diameter and then say with a straight face that it is irrational!
Eight of these are small triangles with roughly equal sides, and 12 are larger and shaped sort of like an ice cream cone.
The resulting porous crystal structure is so fully honeycombed with pockets that a chunk the size of a sugar cube can contain several football fields’ worth of internal surface area.
The moon, however, has an orbit that’s tilted relative to it at an angle of about five degrees.
A human egg cell can reach about 120 microns in diameter, or five one-thousandths of an inch.
Numbers had finally become distinct from geometry; numbers were used to do more than merely measure objects.
The researchers’ new algorithm first traces a 3-D shape’s edges with line segments, then squashes this approximate contour down to 2-D and tries to tile its interior with triangles.
Like a bent arm, the Hoyle state takes the shape of an obtuse triangle with an alpha particle at each vertex.
The measurement suggests that the radius of the Martian core is 1,810 to 1,860 kilometres, roughly half that of Earth’s.
The team gave kids a sheet of paper with just a few basic elements printed on it: some dots here, squiggles there and a rectangle that suggested a drawing frame.
An ice sheet, like any solid, inherently vibrates at some natural frequency.
She is best known for her solution of the sphere packing problem — finding the arrangement of spheres that can take up the largest portion of a volume — in eight dimensions.
Arguably, though, the regular octagon is a little simpler, because it's just a square with the corners cut off.
It is a relative of the rhombicuboctahedron, which is an Archimedean solid that also has 24 vertices with three squares and one equilateral triangle around each vertex.
So the most habitable planet would have roughly twice the mass of the Earth and be between 20% and 30% larger by volume.

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