A View from the Back of the Envelope top

When Length grows a little,
Area grows a lot
Length Area Volume
Lots of dots

1
1
1
1 2
1
1 2
3 22
2
1 2 3
1
1 2 3
4 5 6
7 8 32
2
3
1 2 3 4
1
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 42
2
3
4
1 2 3 4 5 6
1
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 62
2
3
4
5
6
1 2 3 4 5
1
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 52
2
3
4
5
1 2 3 4 5 6 7
1
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
36 37 38 39 40 41 42
43 44 45 46 47 48 72
2
3
4
5
6
7
1 2 3 4 5 6 7 8
1
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 82
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54
55 56 57 58 59 60 61 62 63
64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 92
2
3
4
5
6
7
8
9

1 2 3 4 5 6 7 8 9 10
1
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 102
2
3
4
5
6
7
8
9
10

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu> 

Notes:
  This is a draft of one page of a length/area/volume cluster.
  The length and area numbers refer to different units!  Ouch.
    Or perhaps are dimensionless counting...?


Doables:
  Link
  graph of x, x^2, x^3
  The length and area numbers refer to different units!  Emphasize.
Below,
length is in some nameless unit
1
and area in nameless2 units
(said as "nameless squared")
 

History:
 1998.Apr.29   Created.