The ancient Boreans used a variety of mathematical and measurement systems throughout their floruit. There was a base-5 system initially used by the majority of Boreans, and also a base-13 adopted from the Elves, originally for ceremonial purposes. Later, these would be harmonized into a base-10 system.
Early Borean Base-5
The western Boreans tended to use base-5 numeral systems.
Base 5
0
0I
0II
0III
IV
Base 10
00
01
02
03
04
Base 5
V
VI
VII
VIII
VIV
Base 10
05
06
07
08
09
Base 5
VV
VVI
VVII
VVIII
VVIV
Base 10
10
11
12
13
14
Base 5
VVV
VVVI
VVVII
VVVIII
IVX
Base 10
15
16
17
18
19
Base 5
VX
VXI
VXII
VXIII
IX
Base 10
20
21
22
23
24
Base 5
X
XI
XII
XIII
XIV
Base 10
25
26
27
28
29
Base 5
XV
XVI
XVII
XVIII
XVIV
Base 10
30
31
32
33
34
Base 5
XVV
XVVI
XVVII
XVVIII
XVVIV
Base 10
35
36
37
38
39
Base 5
XVVV
XVVVI
XVVVII
XVVVIII
XIX
Base 10
40
41
42
43
44
Base 5
XX
XXI
XXII
XXIII
XXIV
Base 10
45
46
47
48
49
Base 5
XXV
XXVI
XXVII
XXVIII
XXIX
Base 10
50
51
52
53
54
Base 5
XXX
XXXI
XXXII
XXXIII
XXXIV
Base 10
55
56
57
58
59
Base 5
XXXV
XXXVI
XXXVII
XXXVIII
XXXVIV
Base 10
60
61
62
63
64
Base 5
XXXVV
XXXVVI
XXXVVII
XXXVVIII
XXXVVIV
Base 10
65
66
67
68
69
Base 5
XXXVVV
XXXVVVI
XXXVVVII
XXXVVVIII
IVXL
Base 10
70
71
72
73
74
Base 5
VXL
VXLI
VXLII
VXLIII
IXL
Base 10
75
76
77
78
79
Base 5
XL
XLI
XLII
XLIII
IL
Base 10
80
81
82
83
84
Base 5
L
LI
LII
LIII
LIV
Base 10
85
86
87
88
89
Base 5
LV
LVI
LVII
LIII
LVIV
Base 10
90
91
92
93
94
Base 5
LVV
LVVI
LVVII
LVVIII
LVVIV
Base 10
95
96
97
98
99
Middle Borean Base-5
The western Boreans tended to use base-5 numeral systems.
Base 5
00
01
02
03
04
Base 10
00
01
02
03
04
Base 5
10
11
12
13
14
Base 10
05
06
07
08
09
Base 5
20
21
22
23
24
Base 10
10
11
12
13
14
Base 5
30
31
32
33
34
Base 10
15
16
17
18
19
Base 5
40
41
42
43
44
Base 10
20
21
22
23
24
Base 5
50
Base 10
25
Borean Base-13
The eastern Boreans tended to use base-13 numeral systems.
Base 13
00
01
02
03
04
05
06
07
08
09
0A
0B
0C
Base 10
00
01
02
03
04
05
06
07
08
09
10
11
12
Base 13
10
11
12
13
14
15
16
17
18
19
1A
1B
1C
Base 10
13
14
15
16
17
18
19
20
21
22
23
24
26
Base 13
20
21
22
23
24
25
26
27
28
29
2A
2B
2C
Base 10
26
27
28
29
30
31
32
33
34
35
36
37
38
Base 13
30
31
32
33
34
35
36
37
38
39
3A
3B
3C
Base 10
39
40
41
42
43
44
45
46
47
48
49
50
51
Base 13
40
41
42
43
44
45
46
47
48
49
4A
4B
4C
Base 10
52
53
54
55
56
57
58
59
60
61
62
63
64
Base 13
50
51
52
53
54
55
56
57
58
59
5A
5B
5C
Base 10
65
66
67
68
69
70
71
72
73
74
75
76
77
Base 13
60
61
62
63
64
65
66
67
68
69
6A
6B
6C
Base 10
78
79
80
81
82
83
84
85
86
87
88
89
90
Base 13
70
61
72
73
74
75
76
77
78
79
7A
7B
7C
Base 10
91
92
93
94
95
96
97
98
99
100
101
102
103
Base 13
80
81
82
83
84
85
86
87
88
89
8A
8B
8C
Base 10
104
105
106
107
108
109
110
111
112
113
114
115
116
Base 13
90
91
92
93
94
95
96
97
98
99
9A
9B
9C
Base 10
117
118
119
120
121
122
123
124
125
126
127
128
129
Base 13
A0
A1
A2
A3
A4
A5
A6
A7
A8
A9
AA
AB
AC
Base 10
130
131
132
133
134
135
136
137
138
139
140
141
142
Base 13
B0
B1
B2
B3
B4
B5
B6
B7
B8
B9
BA
BB
BC
Base 10
143
144
145
146
147
148
149
150
151
152
153
154
155
Base 13
C0
C1
C2
C3
C4
C5
C6
B7
C8
C9
CA
CB
CC
Base 10
156
157
158
159
160
161
162
163
164
165
166
167
168
Base 13
100
Base 10
169
Multiplication Table in Base-13
Base 13
10
10
20
30
40
50
60
70
80
90
A0
B0
C0
100
Base 10
13
13
26
39
52
65
78
91
104
117
130
143
156
169
Base 13
0C
0C
1B
2A
39
48
57
66
75
84
93
A2
B1
C0
Base 10
12
12
24
36
48
60
72
84
96
108
120
132
144
156
Base 13
0B
0B
19
27
35
43
51
5C
6A
78
86
94
A2
B0
Base 10
11
11
22
33
44
55
66
77
88
99
110
121
132
143
Base 13
0A
0A
17
24
31
3B
48
55
62
6C
79
86
93
A0
Base 10
10
10
20
30
40
50
60
70
80
90
100
110
120
130
Base 13
09
09
15
21
2A
36
42
4B
57
63
6C
78
84
90
Base 10
09
09
18
27
36
45
54
63
72
81
90
99
108
117
Base 13
08
08
16
1B
26
31
39
44
4C
57
62
6A
75
80
Base 10
08
08
16
24
32
40
48
56
64
72
80
88
96
104
Base 13
07
07
11
18
22
29
33
3A
44
4B
55
5C
66
70
Base 10
07
07
14
21
28
35
42
49
56
63
70
77
84
91
Base 13
06
06
0C
15
1B
24
2A
33
39
42
48
51
57
60
Base 10
06
06
12
18
24
30
36
42
48
54
60
66
72
78
Base 13
05
05
0A
12
17
1C
24
29
31
36
3B
43
48
50
Base 10
05
05
10
15
20
25
30
35
40
45
50
55
60
65
Base 13
04
04
08
0C
13
17
1B
22
26
2A
31
35
39
40
Base 10
04
04
08
12
16
20
24
28
32
36
40
44
48
52
Base 13
03
03
06
09
0B
12
15
18
1B
21
24
27
2A
30
Base 10
03
03
06
09
12
15
18
21
24
27
30
33
36
39
Base 13
02
02
04
06
08
0A
0C
11
13
15
17
19
1B
20
Base 10
02
02
04
06
08
10
12
14
16
18
20
22
24
26
Base 13
01
01
02
03
04
05
06
07
08
09
0A
0B
0C
10
Base 10
01
01
02
03
04
05
06
07
08
09
10
11
12
13
01
02
03
04
05
06
07
08
09
0A
0B
0C
10
Borean Measurements in Base-13
Unit
Equivalents
Imperial conversion
Metric conversion
Inch
1/10th Borean foot
0.975 inches
2.413 cm
Hand
½ span
Span
9¾ inches; ¾ foot; ½ cubit
9.5125 inches; 0.79 feet
Foot
10 inches; ⅔ cubit; ⅓ yard
12.675 inches; 1.05625 feet
32.1945 cm; 0.321945 m
Cubit
16½ inches; 1½ feet; ½ yard
19.0125 inches; 1.584375 feet
0.4829175 m
Ell
23¼ inches; 2¼ feet; 1½ cubits ¾ yard
28.51875 inches; 2.3765625 feet
0.72437625 m
Yard
30 inches; 3 feet; 2 cubits
38.025 inches; 3.16875 feet
0.965835 m
Furlong
Mile
League
Fathom
The average height for a Borean male was about 5½ Borean feet or 3⅔ cubits (about 5.8 Imperial feet or 5’9”, or ~175 cm), with 6 feet or 4 cubits (about 6.34 imperial feet or 6’4”, or ~193 cm) being regarded as unusually tall and 5 feet or 3⅓ cubits (about 5.3 Imperial feet or 5’3”, or ~160 cm) being regarded as unusually short. Average height for a Borean female was about 5 Borean feet or 3⅓ cubits (about 5.3 Imperial feet or 5’3”, or ~160 cm), with 5½ feet or 3⅔ cubits (about 5.8 Imperial feet or 5’9”, or ~175 cm) being regarded as unusually tall and 4½ feet or 3 cubits (about 4.75 Imperial feet or 4’9”, or ~145 cm) being regarded as unusually small.
Borean Currency
The Borean shale was the standard, primary unit of currency all over ancient Borea. In western Borean societies, the shale tended to be divided into five pents, in keeping with the western Borean base-5 numeral system. In eastern Borean and Elfish societies, the shale was more often divided into thirteen lots, in keeping with the eastern Borean base-13 numeral system.
Pictured here is an "Elfin Solar", originally worth 1 shale but eventually a modest collector's piece that could be traded for several times its original value. On the left is the "skyward" side, with a 5-pointed star most likely representing the planet Venus, and wreathed with what looks strikingly like laurel. On the right is the "earthward" side, with a 5-pointed star representing the Earth-womb and surrounded by an ouroboros, which normally represented the yearly cycle of the Sun. The gold circle in the center on both sides surrounded by a field of silver represents the Sun in the sky.
