![]() ![]() (c) What is the largest area the rectangle can have, and what are. (Hint: Write an equation for the line AB.) (b) Express the area of the rectangle in terms of x. (a) Express the y-coordinate of P in terms of x. ^ a b Stromquist, Walter (1989), "Inscribed squares and square-like quadrilaterals in closed curves", Mathematika, 36 (2): 187–197, doi: 10. Transcribed Image Text: The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 30 units long.^ a b c d Matschke, Benjamin (2014), "A survey on the square peg problem", Notices of the American Mathematical Society, 61 (4): 346–352, doi: 10.1090/noti1100.^ a b Hartnett, Kevin (June 25, 2020), "New geometric perspective cracks old problem about rectangles", Quanta Magazine, retrieved.(1944), "On certain geometrical properties of closed curves", Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo. ^ Emch, Arnold (1916), "On some properties of the medians of closed continuous curves formed by analytic arcs", American Journal of Mathematics, 38 (1): 6–18, doi: 10.2307/2370541, JSTOR 2370541, MR 1506274.(1911), "Über einige Aufgaben der Analysis situs", Verhandlungen der Schweizerischen Naturforschenden Gesellschaft (in German), 94: 197 Let C contains many inscribed rectangles. As of 2020, the general case remains open. Some early positive results were obtained by Arnold Emch and Lev Schnirelmann. The problem was proposed by Otto Toeplitz in 1911. The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. (more unsolved problems in mathematics) Example: The black dashed curve goes through all corners of several blue squares. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |