In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square...

equal area. The study of equidissections began in the late 1960s with Monsky's theorem, which states that a square cannot be equidissected into an odd number...

Minkowski's second theorem (geometry of numbers) Minkowski–Hlawka theorem (geometry of numbers) Monsky's theorem (discrete geometry) Pick's theorem (geometry)...

analytic functions with few distinct values The fundamental theorem of algebra Monsky's theorem (4th edition) Van der Waerden's conjecture (6th edition)...

theorem on a square derived from two squares sharing a vertex Midsquare quadrilateral, a polygon whose edge midpoints form a square Monsky's theorem,...

tight closure does not commute with localization. The first proof of Monsky's theorem, published in 1970, which states that a square cannot be divided into...

have restrictions on the possible numbers of triangles. For example, Monsky's theorem states that there is no odd equidissection of a square. Among dissection...

Menelaus' theorem Miquel's theorem Mittenpunkt Modern triangle geometry Monsky's theorem Morley centers Morley triangle Morley's trisector theorem Musselman's...

{\displaystyle m} is even, by affine invariance of equidissection and Monsky's theorem on equidissections of squares. More generally an n {\displaystyle n}...

protocols. Sperner's lemma is one of the key ingredients of the proof of Monsky's theorem, that a square cannot be cut into an odd number of equal-area triangles...

by two squares and four 45° rhombi. In a generalization of Monsky's theorem, Paul Monsky (1990) proved that no zonogon has an equidissection into an...

this is the notorious tripod packing problem. Chapter five considers Monsky's theorem on the impossibility of partitioning a square into an odd number of...

(precursors of the crystalline theory, introduced in various forms by Dwork, Monsky, Washnitzer, Lubkin and Katz) particularly in Dwork's work. Such differential...

Craig (1990), "Tight closure, invariant theory, and the Briançon–Skoda theorem", Journal of the American Mathematical Society, 3 (1): 31–116, doi:10.2307/1990984...

this problem has not been brought to a successful resolution. Tunnell's theorem provides an easily testable criterion for determining whether a number...

problem. Stein is also known as one of the independent discoverers of Fáry's theorem, and for his contributions to equidissection, the partition of polygons...