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Proportional pie-cutting

Steven J. Brams, Michael A. Jones, Christian Klamler
2007 International Journal of Game Theory  
We will use vertical, parallel cuts to divide a cake into pieces, and radial cuts from the center to divide a pie into wedge-shaped pieces.  ...  David Gale (1993) was perhaps the first to suggest that there is a difference between cake and pie cutting.  ...  Proportional Pie-Cutting Steven J.Brams et al.  ... 
doi:10.1007/s00182-007-0108-z fatcat:dsxpbgxswfhhhhmcjkmcwqpwza

Eccentric pie charts and an unusual pie cutting [article]

Sándor Bozóki
2019 arXiv   pre-print
The method is illustrated on a special pie cutting problem, and is applicable to a wide class of nonlinear, non-polynomial systems.  ...  The eccentric pie chart, a generalization of the traditional pie chart is introduced. An arbitrary point is fixed within the circle and rays are drawn from it.  ...  2 (2n + 1) x 2n+1 = π 2 − x − 1 6 x 3 − 3 40 x 5 + O(x 7 ), (|x| < 1) (7) Pie cutting with a multi-blade cutter Let us solve the 40-35-25% pie-cutting problem from the beginning of the paper.  ... 
arXiv:1904.02535v1 fatcat:rwarmeewr5emjl63notey7rrdq

Page 465 of American Journal of Pharmacy and the Sciences Supporting Public Health Vol. 30, Issue [page]

1858 American Journal of Pharmacy and the Sciences Supporting Public Health  
Bridges was called upon to determine the quantitative proportion of the arsenic, and as he had not reserved any of the pie, he could only determine the proportion remaining in the unexhausted liquid of  ...  How much had been removed in the numerous preliminary experiments could " not be determined, but the proportion isolated was amply sufficient to prove that the pie had been effectually poisoned.  ... 

Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond

Julius B. Barbanel, Steven J. Brams
2004 Mathematical Social Sciences  
The minimal number of parallel cuts required to divide a cake into n pieces is n À 1.  ...  An extension of this procedure leads to a 4-person division, using three parallel cuts, which makes at most one person envious.  ...  When cutting a pie, by contrast, we assume that the pie is a disk and that all cuts are between the center and a point on the circumference (as we would cut a real pie).  ... 
doi:10.1016/j.mathsocsci.2004.03.006 fatcat:kzdphduf25hzpeizvzhik3prai

Page 67 of Arthur's Home Magazine Vol. 9, Issue [page]

1857 Arthur's Home Magazine  
When you have rolled your paste for the covering of an equal thick- ness, in proportion to the contents of your pie (half an inch is about correct for the above description,) fold the cover in two, lay  ...  on the half of your pie, turn the other half over, press slightly with your thumb round the rim, cut neatly the rim of your paste, form rather a thick edge, which mark with a knife about every quarter  ... 

Page 417 of Journal of Family and Consumer Sciences Vol. 18, Issue 7 [page]

1926 Journal of Family and Consumer Sciences  
In order to determine the comparative digestibility of pie crust, pie crust and muffins made from the same kind and proportion of ingredients were used in a digestion experi- ment with two normal women  ...  The apples were peeled and quartered, a thin sample was cut from each quarter, and these samples were dried for five days in a Freas electric oven at a temperature of 425°F.  ... 

Sensory Evaluation of Snacks Produced From Wheat-Breadfruit Flour and Nutritional Composition of the Flour Blends

Folorunso, Adekunle A, Habeeb, Aisha S, Ajayi, Odunola T
2019 Agriculture and Food Sciences Research  
Two different snacks, meat pie and chin-chin were produced using three different mixing proportions (50:50,30:70 & 70:30) of wheat-breadfruit flour blends for each making a total of six snack samples respectively  ...  There are significant difference at (p<0.05) in the results for sensory evaluation of chin chin and meat pie samples.  ...  Produce the flour blends of different proportions. iii.  ... 
doi:10.20448/journal.512.2019.61.89.97 fatcat:hv42dr6sxfearfeifejfc75abe

Page 614 of Arthur's Home Magazine Vol. 43, Issue 10 [page]

1875 Arthur's Home Magazine  
If it does this it is good, and your ingredients have been in proportion. I always flour the tin, so I can slip the pie off ona cloth or on a paper to cool.  ...  To-morrow I | will tell you how I make pie-crust.  ... 

Page 356 of The Westminster Review Vol. 22, Issue 2 [page]

1835 The Westminster Review  
Alban’s, caused the woods to be cut down. The first line is obscure.  ...  ’ referred to the Cornish predilection for pies of all materials ; as squab-pie, herby-pie, pilchard-pie, mugetty-pie, &c.  ... 

Mind the Gap: Cake Cutting With Separation [article]

Edith Elkind, Erel Segal-Halevi, Warut Suksompong
2021 arXiv   pre-print
In addition, we consider the division of a pie (i.e., a circular cake) and show that an ordinal relaxation of maximin share fairness can be achieved.  ...  We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated  ...  However, in pie cutting, unlike in cake cutting, an MMS-fair allocation does not necessarily exist.  ... 
arXiv:2012.06682v2 fatcat:uxcomwc2onhvhofrfjsanbxr6e

Replacing bar graphs of continuous data with more informative graphics: Are we making progress? [article]

Nico Riedel, Robert Schulz, Vartan Kazezian, Tracey L Weissgerber
2022 bioRxiv   pre-print
plots, histograms, pie charts, and flow charts.  ...  Bar graphs are more often used incorrectly to display continuous data than they are used correctly to display counts or proportions.  ...  Cutting the axis is potentially problematic for counts and proportions, as this alters viewers' perception of the count or proportion.  ... 
doi:10.1101/2022.03.14.484206 fatcat:qtnzmdvbxjcbbb4hsefpil3yee

Page 286 of Friends' Intelligencer Vol. 58, Issue 18 [page]

1901 Friends' Intelligencer  
Gointo a restaurant and ask for a ‘‘cut of standard,’’ and the waiter will bring you a piece of apple pie. He knows what standard pie is.  ...  Don’t you see that you must have a bottom of pastry and that there isa just proportion of crust to filling that must not be deviated from one iota or your pie is inartistic and an offense against the laws  ... 

Page 136 of Arthur's Home Magazine Vol. 52, Issue 2 [page]

1884 Arthur's Home Magazine  
Put the meat in omelet in the proportion of a tablespoonful of meat to an egg, seasoning with sage. For meat-pies, omit the chopping.  ...  Cut the meat in mouthfuls; add potatoes to your liking; line a deep dish with pie-crust, put in your meat, potatoes, and gravy enough to nearly fill the dish, | cover and bake—not forgetting the hole in  ... 

Page 441 of Southern Agriculturist, Horticulturist, and Register of Rural Affairs Vol. 4, Issue 8 [page]

1831 Southern Agriculturist, Horticulturist, and Register of Rural Affairs  
No grain is given to these animals without its due proportion of cut hay and straw.  ...  The stems are easily prepared for the pie or pudding, by strip- ping off the skin, commencing at either end, which slips off very * It may be observed, that this latter practice is also common with mil  ... 

Page 26 of Horticulturist and Journal of Rural Art and Rural Taste Vol. 9, Issue 1 [page]

1854 Horticulturist and Journal of Rural Art and Rural Taste  
No wonder that the vigor of our plants was increased in a wonderful proportion! As soon as any buds appeared they were taken off—the leaves were cut as often as they became large enough for use.  ...  CULTURE OF PIE PLANT—RHEUM.  ... 
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