Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
Papers published on a yearly basis
Papers
More filters
01 Jan 1981
100 citations
TL;DR: A family of natural methods meeting the requirements for impartial division, for a division among four or more participants, are proposed.
99 citations
TL;DR: Geometry-sensing mechanisms control both the decision to enter into cell division and the physical orientation of the chromosome segregation machinery, suggesting that signals controlling cell division may be linked to the mechanisms that ensure proper chromosome segregation.
99 citations
Journal Article•
TL;DR: In this paper, a 2-person surplus procedure (SP) was proposed to divide a cake among n people with n-1 cuts (the minimum number of cuts) and compared with a 3-party surplus procedure, which induces players to be truthful in order to maximize their minimum allocations.
Abstract: Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser’s preferences, whereas the chooser can generally obtain more. By comparison, a new 2person surplus procedure (SP), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus—the part that remains after each player receives 50%—by giving each person exactly the same proportion of the surplus as he or she values it. For n ≥ 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.
99 citations
Book•
01 Jan 2000
TL;DR: In this article, the empty number line is used to make sense of numbers and counting and coming to know numbers, and the system of symbols is used for teaching and teaching approaches.
Abstract: 1. Making sense of numbers 2. Counting and coming to know numbers 3. Towards a system of symbols. 4. Addition and subtraction 5. The empty number line 6. Multiplication and Division 7. Written calculations 8. Teaching approaches.
98 citations