Since seventeen is a Fermat prime, regularheptadecagons can beconstructed with acompass and unmarked ruler. This was proven byCarl Friedrich Gauss and ultimately led him to choose mathematics over philology for his studies.[6][7]
The minimum possible number of givens for asudoku puzzle with a unique solution is 17.[8][9]
Either 16 or 18unit squares can be formed into rectangles with perimeter equal to the area; and there are no othernatural numbers with this property. ThePlatonists regarded this as a sign of their peculiar propriety; andPlutarch notes it when writing that thePythagoreans "utterly abominate" 17, which "bars them off from each other and disjoins them".[20]
17 is the least for theTheodorus Spiral to complete onerevolution.[21] This, in the sense ofPlato, who questioned why Theodorus (his tutor) stopped at when illustrating adjacentright triangles whose bases areunits and heights are successivesquare roots, starting with. In part due to Theodorus's work as outlined in Plato'sTheaetetus, it is believed that Theodorus had proved all the square roots of non-square integers from3 to 17 areirrational by means of this spiral.
In three-dimensional space, there are seventeen distinctfully supported stellations generated by anicosahedron.[22] The seventeenth prime number is59, which is equal to the total number of stellations of the icosahedron byMiller's rules.[23][24] Without counting the icosahedron as azeroth stellation, this total becomes58, a count equal to the sum of the first seven prime numbers (2 + 3 + 5 + 7 ... + 17).[25] Seventeen distinct fully supported stellations are also produced bytruncated cube andtruncated octahedron.[22]
Seventeen is also the number of four-dimensionalparallelotopes that arezonotopes. Another 34, or twice 17, areMinkowski sums of zonotopes with the24-cell, itself the simplest parallelotope that is not a zonotope.[26]
17 was described atMIT as "the least random number", according to theJargon File.[32] This is supposedly because, in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice. This study has been repeated a number of times.[33]
^John H. Conway and Richard K. Guy,The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compasses."
^McGuire, Gary (2012). "There is no 16-clue sudoku: solving the sudoku minimum number of clues problem".arXiv:1201.0749 [cs.DS].
^McGuire, Gary; Tugemann, Bastian; Civario, Gilles (2014). "There is no 16-clue sudoku: Solving the sudoku minimum number of clues problem via hitting set enumeration".Experimental Mathematics.23 (2):190–217.doi:10.1080/10586458.2013.870056.S2CID8973439.
^Senechal, Marjorie; Galiulin, R. V. (1984). "An introduction to the theory of figures: the geometry of E. S. Fedorov".Structural Topology (in English and French) (10):5–22.hdl:2099/1195.MR0768703.
