Authors: Matthew, Rebekah, Deepu, Brian, Fiona, Miracle, Carsten, Zoe
Is this a fair die? The Riverbend gang is bound to find out. We are testing cylindrical dice. Will the die land on all the sides the same amount of times?
Here we do a lot of math and Amanda makes it easier for us to learn math related things. The people who participate are Fiona, Rebekah, Matthew, Deepu, Brian, Travis, Victoria, Valeria, Laura, Zoe, Jennifer, Martha, and Jimmy.
We made our dice, then we tossed them in the air about 50 to 100 times. On a piece of paper we recorded how many times the die landed on each side. For example if you tossed the die in the air 50 times and it came up 16 times on the side,you would write the fraction 16/50 to represent the proportion of times it landed on its side. Then you would turn the fraction into a decimal. To find the decimal you have to divide the numerator by the denominator. In this case the answer would be 0.32. If the decimal was between 0.199 and 0.467 it would be a candidate or else it would be a reject.
Die code | Candidate/Reject | Material | Description | Height (Inches) | Diameter (Inches) | Height / Diameter | Times Tested | # of 1s | # of 2s | # of 3s (Lateral surface) | Fraction of 1s | Fraction of 2s | Fraction of 3s | Notes |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B.004 | Reject | 1 felt pad | height = 1/4 of radius | 0.125 | 1 | 0.13 | 50 | 28 | 22 | 0 | 0.56 | 0.44 | 0 | |
A.015 | Reject | wood dowel | see Measurements >> | 0.25 | 1.125 | 0.22 | 50 | 22 | 27 | 1 | 0.44 | 0.54 | 0.02 | |
A.014 | Reject | wood dowel | equal-area | 0.188 | 0.75 | 0.25 | 50 | 24 | 22 | 4 | 0.48 | 0.44 | 0.08 | |
A.016 | Reject | wood dowel | equal-area | 0.25 | 1 | 0.25 | 50 | 23 | 27 | 0 | 0.46 | 0.54 | 0 | |
C.005 | Reject | PVC pipe | Travis's conjecture | 0.375 | 1.063 | 0.35 | 51 | 36 | ? | ? | 0.71 | ? | ? | Information partly illegible; also, testing suspicious |
C.001 | Candidate | PVC pipe sandwiched between metal washers | Von Neumann's conjecture | 0.438 | 1 | 0.44 | 50 | 15 | 17 | 19 | 0.3 | 0.34 | 0.38 | |
A.017 | Reject | 3/4" wood dowel (1 1/16" high) sandwiched between felt pads | Von Neumann's conjecture | 0.438 | 1 | 0.44 | 26 | 1 | 0 | 25 | 0.04 | 0 | 0.96 | Testing suspicious |
B.005 | Reject | 4 felt pads | Von Neumann's conjecture | 0.875 | 2 | 0.44 | 50 | 22 | 19 | 9 | 0.44 | 0.38 | 0.18 | |
A.001 | Candidate | wood dowel | radius = height | 0.375 | 0.75 | 0.5 | 50 | 17 | 19 | 14 | 0.34 | 0.38 | 0.28 | |
A.005 | Candidate | wood dowel | Travis's conjecture | 0.5 | 1 | 0.5 | 50 | 16 | 17 | 17 | 0.32 | 0.34 | 0.34 | |
B.001 | Candidate | metal washer sandwiched between felt pads | radius = height | 0.5 | 1 | 0.5 | 55 | 18 | 19 | 18 | 0.33 | 0.35 | 0.33 | |
B.002 | Candidate | 5 felt pads | radius = height | 1 | 2 | 0.5 | 50 | 19 | 10 | 21 | 0.38 | 0.2 | 0.42 | |
A.008 | Reject | wood dowel | radius = height | 0.375 | 0.75 | 0.5 | 53 | 16 | 26 | 11 | 0.3 | 0.49 | 0.21 | |
A.004 | Candidate | 5/8 wood dowel, 3/8 felt pad | radius = height | 0.5 | 0.938 | 0.53 | 50 | 15 | 17 | 18 | 0.3 | 0.34 | 0.36 | |
A.004 | Candidate | 5/8 wood dowel, 3/8 felt pad | radius = height | 0.5 | 0.938 | 0.53 | 50 | 16 | 16 | 18 | 0.32 | 0.32 | 0.36 | |
B.003 | Candidate | 3 felt pads | radius = height | 0.563 | 1 | 0.56 | 50 | 18 | 14 | 18 | 0.36 | 0.36 | 0.28 | |
C.003 | Reject | PVC pipe | see Measurements >> | 0.625 | 1.063 | 0.59 | 50 | 14 | 13 | 23 | 0.28 | 0.26 | 0.46 | |
A.020 | Candidate | wood dowel | diameter x (1 / phi) = height | 0.773 | 1.25 | 0.62 | 50 | 13 | 15 | 22 | 0.26 | 0.3 | 0.44 | |
A.019 | Candidate | wood dowel | diameter x (1 / phi) = height | 0.464 | 0.75 | 0.62 | 50 | 17 | 13 | 20 | 0.34 | 0.26 | 0.4 | |
A.002 | Candidate | wood dowel | Travis's conjecture | 0.625 | 1 | 0.63 | 54 | 19 | 20 | 15 | 0.35 | 0.37 | 0.28 | |
C.006 | Reject | PVC pipe | Travis's conjecture | 0.625 | 1 | 0.63 | 50 | 9 | 7 | 34 | 0.18 | 0.14 | 0.68 | |
A.003 | Candidate | wood dowel | Travis's conjecture | 0.688 | 1.063 | 0.65 | 103 | 29 | 31 | 43 | 0.28 | 0.3 | 0.42 | |
C.002 | Candidate | PVC pipe sandwiched between metal washers | see Measurements >> | 0.75 | 1 | 0.75 | 50 | 15 | 15 | 20 | 0.3 | 0.3 | 0.4 | |
A.007 | Reject | wood dowel | see Measurements >> | 0.938 | 1.063 | 0.88 | 50 | 7 | 3 | 40 | 0.14 | 0.06 | 0.8 | |
A.006 | Reject | wood dowel | diameter = height | 1.063 | 1.063 | 1 | 50 | 5 | 5 | 40 | 0.1 | 0.1 | 0.8 | |
A.009 | Reject | wood dowel | diameter = height | 0.75 | 0.75 | 1 | 50 | 4 | 3 | 43 | 0.08 | 0.06 | 0.86 | |
A.010 | Reject | wood dowel | diameter = height | 0.75 | 0.75 | 1 | 50 | 1 | 4 | 45 | 0.02 | 0.08 | 0.9 | |
A.012 | Reject | wood dowel | diameter = height | 1.063 | 1.063 | 1 | 50 | 7 | 8 | 35 | 0.14 | 0.16 | 0.7 | |
A.013 | Reject | wood dowel | see Measurements >> | 1.125 | 1.063 | 1.06 | 51 | 5 | 7 | 39 | 0.1 | 0.14 | 0.76 | |
A.011 | Reject | wood dowel | see Measurements >> | 1.563 | 1.063 | 1.47 | 51 | 9 | 11 | 31 | 0.18 | 0.22 | 0.61 | |
C.004 | Reject | PVC pipe | see Measurements >> | 2.188 | 1 | 2.19 | 50 | 0 | 0 | 50 | 0 | 0 | 1 | Unevenly cut - smallest height listed |
A.018 | Reject | 3/4" wood dowel (2" high) sandwiched between 4 felt pads on each end | see Measurements >> | 3.563 | 1 | 3.56 | 50 | 0 | 0 | 50 | 0 | 0 | 1 |
We would remake our dice out of different materials to see if the different materials really did make a difference in the ratios.