tetrahedron kites and the mathematics embedded within. by art mabbott seattle schools and park city...
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Tetrahedron Kites
And the mathematics embedded within.By
Art MabbottSeattle Schools and Park City Math Institute
QuadraticMust be aN
18368
17287
16216
15155
14104
1363
1232
1111
000
2nd
Difference1st
DifferenceTriangular Numbers
Level
N*(N+1)/2So…
N*(N+1)N
724*9368
564*7287
423*7216
5*6303*5155
4*5202*5104
3*4122*363
2*361*332
1*221*111
0*100*000
Factoring TwiceTri #’s
Twice Tri #’s
Factoring Tri #’s
Triangular Numbers
Level
1105522010
19451659
18361208
1728847
1621566
1515355
1410204
136103
12342
11111
0000
3rd
Difference2nd
Difference1st
Difference
Tetrahedron Numbers
N*(N+1)*(N+2)[N*(N+1)*(N+2)]/6N
720=8*9*103602401208
504=7*8*9252168847
336=6*7*8168112566
210=5*6*710570355
120=4*5*66040204
60=3*4*53020103
24=2*3*412842
6=1*2*33211
0=0*1*20000
Six timesThree times
Twice
FactorsTetrahedron Numbers
Let’s Make the Kites
Number of
Straws
Length of a Side
PerimeterArea of a Face
Total Surface
AreaTotal Volume
1 1 31
Triangle 4 1 Tetrahedron
2 2 6 4 16 8
3 3 9 9 36 27
4 4 12 16 64 64
5 5 15 25 100 125
6 6 18 36 144 216
7 7 21 49 196 343
8 8 24 64 256 512
9 9 27 81 324 729
10 10 30 100 400 1000
20 20 60 400 1600 8000
100 100 300 10000 40000 1000000
… n 3n n 2 4n 2 n 3
Numberof Straws
UpTetrahedrons Octahedron
DownTetrahedrons
TotalVolume
1 1 - - 1
2 4 = 1 + 3 1(4) - 8
3 10 = 1 + 3 + 6 4(4) 1 27
4 20 = 1 + 3 + 6 + 10 10(4) 4 64
535 = 1 + 3 + 6 +
10+ 15
20(4) 10 125
6 56 35(4) 20 216
7 84 56(4) 35 343
8 120 84(4) 56 512
9 165 120(4) 84 729
10 220 165(4) 120 1000
20 1540 1330(4) 1140 8000
100 171700 166650(4) 161700 1000000
… (n)(n+1)(n+2)/6 (4)((n-1)(n)(n+1)/6) ((n-2)(n-1)(n))/6 n3
(n3+3n2+2n)/6 (4n3-4n)/6 (n3-3n2+2n)/6
Art [email protected] contact me:(206) 605-7393
http:mabbott.org/mathguy.htmhttp:mabbott.org/tetprep.htm
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