![]() ![]() Of the fifth Platonic solid, the dodecahedron, Plato obscurely remarked, ".the god used for arranging the constellations on the whole heaven". Moreover, the cube's being the only regular solid that tessellates Euclidean space was believed to cause the solidity of the Earth. These clumsy little solids cause dirt to crumble and break when picked up in stark difference to the smooth flow of water. By contrast, a highly nonspherical solid, the hexahedron (cube) represents "earth". Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. Air is made of the octahedron its minuscule components are so smooth that one can barely feel it. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). ![]() Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Plato wrote about them in the dialogue Timaeus c.360 B.C. The Platonic solids are prominent in the philosophy of Plato, their namesake. In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist. Other evidence suggests that he may have only been familiar with the tetrahedron, cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. Some sources (such as Proclus) credit Pythagoras with their discovery. Send us feedback about these examples.The ancient Greeks studied the Platonic solids extensively. These examples are programmatically compiled from various online sources to illustrate current usage of the word 'congruent.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Department of Education, as well as mandate yearly increases congruent to inflation. ![]() ![]() 2021 Their bill would incentivize states to raise minimum salaries to $60,000 for public K-12 teachers, through a grant program at the U.S. is not 15 p.m., but 3 is congruent (essentially, equal) with 15 (mod 12). Steven Aquino, Forbes, 8 June 2022 Surprisingly, the answers given by male and female subjects regarding sociosexual behaviour and mating preferences are predominantly congruent. 2023 Beyond the broader sociocultural discussion on disability and financial solvency, the reality is the need for Apple’s best-of-breed accessibility support unfortunately isn’t always congruent with the ability to actually procure the tools that provide it. David James, Anchorage Daily News, 18 June 2023 In another example of congruent storytelling in the Triple H Era, Charlotte was seen smiling approvingly on the outside of the ring similar to Sasha Banks when Bianca Belair snatched the torch from up under Charlotte’s fellow horsewoman at WrestleMania 37. 2022 In some instances, this leads to interesting and sometimes not entirely congruent recollections of events told by different participants. Patrick Honner, Quanta Magazine, 21 Nov. 2022 Since the triangle is scissors congruent to the rectangle and the rectangle is scissors congruent to the square, the triangle is scissors congruent to the square. Recent Examples on the Web In other words, scissors congruence is symmetric: If shape A is scissors congruent to shape B, then shape B is also scissors congruent to shape A. ![]()
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