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Vol.5, No.9, 963-971 (2013) Natural Science
http://dx.doi.org/10.4236/ns.2013.59117
Relationship of nine constants
Michael Snyder
Department of Physics and Astronomy, University of Louisville, Louisville, USA; [email protected]
Received 25 June 2013; revised 25 July 2013; accepted 4 August 2013
Copyright © 2013 Michael Snyder. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
Through the process of trial and error, four
unitless equations made up of nine constants
have been found with exact ans wers. The related
constants are the Speed of Light [1], the Planck
constant [2], Wien’s displacement constant [3],
Avogadro’s number [4], the universal Gravity
constant [5], the Ampere constant [6], the Fara-
day constant [7], the G as constant [8] and Apery’s
constant [9].
Keywords: Planck; Wien; Avogadro; Faraday;
Apery; Ampere
1. INTRODUCTION
At the end of the spring semester 2013, I had found an
expression of a few physical constants that gave the cor-
rect value of the universal Gravity constant [5]. I shared
my findings with my classmates and they all pointed out
the units were incorrect.
This started the search for a unitless expression of
physical constants similar in form to the Fine Structure
constant but with more constants.
In the context of this paper, the term unitless is defined
as all the exponents of the units on the left hand side of
the equation are equal to zero and the right hand side of
the equation is represented by only a numeric expression.
2. MAIN BODY
The first few equations were found by trial and error.
One would literally examine a listing of physical con-
stants and guess which set of constants multiplied to-
gether and divided by another set of multiplied constants
produces an answer with units raised to the zero power.
I had the limited success of finding the Fine Structure
constant over and over again. At this point I changed my
strategy by writing a program that would try every com-
bination of a set of constants within a certain integer
range of exponents, with its dimensionality equal to a
selected SI unit. This strategy worked in the sense that it
produced a large set of equations, of the selected con-
stants that had the required SI units of seconds or meters,
etc.
The programming process and the testing the programs
happened over a few weeks and various sets of physical
constants where tried. Overall the physical constants that
produced the most equations were selected to be in the
final set of nine presented in this paper.
A few things happened concurrently that allowed me
to find the equations presented in this paper. One was
that I started using a unit of an ampere-mole as a range
extender in my search programs. The derived unit could
be removed from the final answers yet its presence in the
program allowed more equations to be found.
The second was that it occurred to me that the struc-
ture of the programs that I had written; could search for
unitless equations too. The third was that I added the
Faraday constant to the primary set of search constants. I
intended to use the Faraday constant as a more robust
replacement for the derived ampere-mole constant, and
was hoping for similar results.
A few minutes later, the first of many unitless equa-
tions appeared on the screen. Through the process of trial
and error I had found a set of eight physical constants
that produced unitless equations.
Once a pattern was found in the first few equations, a
new program in the Cuda GPU language was written to
find unitless combinations expressed as the powers of the
constants. A program listing is included for completeness
as Appendix I.
A set of 200 unitless equations are shown in Tab le 1 ,
and Eq.1 through Eq.4 are the results of the reduced row
echelon form of Tab le 1 . The reduced row echelon op-
eration on Table 1, results with two rows.
Eq.1 represents the first row and Eq.2 represents the
second row of the reduced row echelon form. Eq.3
represents the multiplication of the Eq.1 and Eq.2 and
Eq.4 represents the quotient of Eq.1 and Eq. 2. One can
Copyright © 2013 SciRes. OPEN ACCESS
M. Snyder / Natural Science 5 (2013) 963-971
964
Table 1. A family of unitless equations.
Index Number Ln (c0 h
0 A
0 R
0 w
0 G
0 N
0 F
0) = value
1 0 0 0 0 0 0 0 0 0
2 −64 −70 −2 69 69 −1 −71 2 0.29664
3 −128 −140 −4 138 138 −2 −142 4 0.59328
4 193 211 6 −208 −208 3 214 −6 0.71252
5 −192 −210 −6 207 207 −3 −213 6 0.88992
6 129 141 4 −139 −139 2 143 −4 1.0092
7 65 71 2 −70 −70 1 72 −2 1.3058
8 1 1 0 −1 −1 0 1 0 1.6024
9 −63 −69 −2 68 68 −1 −70 2 1.8991
10 −127 −139 −4 137 137 −2 −141 4 2.1957
11 194 212 6 −209 −209 3 215 −6 2.315
12 −191 −209 −6 206 206 −3 −212 6 2.4924
13 130 142 4 −140 −140 2 144 −4 2.6116
14 66 72 2 −71 −71 1 73 −2 2.9082
15 2 2 0
−2 −2
0 2 0 3.2049
16 −62 −68 −2 67 67 −1 −69 2 3.5015
17 −126 −138 −4 136 136 −2 −140 4 3.7982
18 195 213 6 −210 −210 3 216 −6 3.9174
19 −190 −208 −6 205 205 −3 −211 6 4.0948
20 131 143 4 −141 −141 2 145 −4 4.214
21 67 73 2 −72 −72 1 74 −2 4.5107
22 3 3 0 −3 −3 0 3 0 4.8073
23 −61 −67 −2 66 66 −1 −68 2 5.1039
24 −125 −137 −4 135 135 −2 −139 4 5.4006
25 196 214 6 −211 −211 3 217 −6 5.5198
26 −189 −207 −6 204 204 −3 −210 6 5.6972
27 132 144 4 −142 −142 2 146 −4 5.8165
28 68 74 2 −73 −73 1 75 −2 6.1131
29 4 4 0 −4 −4 0 4 0 6.4097
30 −60 −66 −2 65 65 −1 −67 2 6.7064
31 −124 −136 −4 134 134 −2 −138 4 7.003
32 197 215 6 −212 −212 3 218 −6 7.1223
33 −188 −206 −6 203 203 −3 −209 6 7.2997
34 133 145 4 −143 −143 2 147 −4 7.4189
35 69 75 2 −74 −74 1 76 −2 7.7155
36 5 5 0 −5 −5 0 5 0 8.0122
37 −59 −65 −2 64 64 −1 −66 2
8.3088
38 −123 −135 −4 133 133 −2 −137 4 8.6055
39 198 216 6 −213 −213 3 219 −6 8.7247
40 −187 −205 −6 202 202 −3 −208 6 8.9021
41 134 146 4 −144 −144 2 148 −4 9.0213
42 70 76 2 −75 −75 1 77 −2 9.318
43 6 6 0 −6 −6 0 6 0 9.6146
44 −58 −64 −2 63 63 −1 −65 2 9.9113
45 −122 −134 −4 132 132 −2 −136 4 10.208
46 199 217 6 −214 −214 3 220 −6 10.327
47 −186 −204 −6 201 201 −3 −207 6 10.505
48 135 147 4 −145 −145 2 149 −4 10.624
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M. Snyder / Natural Science 5 (2013) 963-971 965
Continued
49 71 77 2 −76 −76 1 78 −2 10.92
50 7 7 0 −7 −7 0 7 0 11.217
51 −57 −63 −2 62 62 −1 −64 2 11.514
52 −121 −133 −4 131 131 −2 −135 4 11.81
53 200 218 6 −215 −215 3 221 −6 11.93
54 −185 −203 −6 200 200 −3 −206 6 12.107
55 136 148 4 −146 −146 2 150 −4 12.226
56 72 78 2 −77 −77 1 79 −2 12.523
57 8 8 0 −8 −8 0 8 0 12.819
58 −56 −62 −2 61 61 −1 −63 2 13.116
59 −120 −132 −4 130 130 −2 −134 4 13.413
60 201 219 6 −216 −216 3 222 −6 13.532
61 −184 −202 −6 199 199 −3 −205 6
13.709
62 137 149 4 −147 −147 2 151 −4 13.829
63 73 79 2 −78 −78 1 80 −2 14.125
64 9 9 0 −9 −9 0 9 0 14.422
65 −55 −61 −2 60 60 −1 −62 2 14.719
66 −119 −131 −4 129 129 −2 −133 4 15.015
67 202 220 6 −217 −217 3 223 −6 15.134
68 −183 −201 −6 198 198 −3 −204 6 15.312
69 138 150 4 −148 −148 2 152 −4 15.431
70 74 80 2 −79 −79 1 81 −2 15.728
71 10 10 0 −10 −10 0 10 0 16.024
72 −54 −60 −2 59 59 −1 −61 2 16.321
73 −118 −130 −4 128 128 −2 −132 4
16.618
74 203 221 6 −218 −218 3 224 −6 16.737
75 −182 −200 −6 197 197 −3 −203 6 16.914
76 139 151 4 −149 −149 2 153 −4 17.034
77 75 81 2 −80 −80 1 82 −2 17.33
78 11 11 0 −11 −11 0 11 0 17.627
79 −53 −59 −2 58 58 −1 −60 2 17.923
80 −117 −129 −4 127 127 −2 −131 4 18.22
81 204 222 6 −219 −219 3 225 −6 18.339
82 −181 −199 −6 196 196 −3 −202 6 18.517
83 140 152 4 −150 −150 2 154 −4 18.636
84 76 82 2 −81 −81 1 83 −2 18.933
85 12 12 0 −12 −12 0 12 0 19.229
86 −52 −58 −2 57 57 −1 −59 2 19.526
87 −116 −128 −4 126 126 −2 −130 4 19.823
88 205 223 6 −220 −220 3 226 −6 19.942
89 −180 −198 −6 195 195 −3 −201 6 20.119
90 141
153 4 −151 −151 2 155 −4 20.238
91 77 83 2 −82 −82 1 84 −2 20.535
92 13 13 0 −13 −13 0 13 0 20.832
93 −51 −57 −2 56 56 −1 −58 2 21.128
94 −115 −127 −4 125 125 −2 −129 4 21.425
95 206 224 6 −221 −221 3 227 −6 21.544
96 −179 −197 −6 194 194 −3 −200 6 21.722
97 142 154 4 −152 −152 2 156 −4 21.841
98 78 84 2 −83 −83 1 85 −2 22.137
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M. Snyder / Natural Science 5 (2013) 963-971
966
Continued
99 14 14 0 −14 −14 0 14 0 22.434
100 −50 −56 −2 55 55 −1 −57 2 22.731
101 −114 −126 −4 124 124 −2 −128 4 23.027
102 207 225 6 −222 −222 3 228 −6 23.147
103 −178 −196 −6 193 193 −3 −199 6 23.324
104 143 155 4 −153 −153 2 157 −4 23.443
105 79 85 2 −84 −84 1 86 −2 23.74
106 15 15 0 −15 −15 0 15 0 24.037
107 −49 −55 −2 54 54 −1 −56 2 24.333
108 −113 −125 −4 123 123 −2 −127 4 24.63
109 208 226 6 −223 −223 3 229 −6 24.749
110 −177 −195 −6 192 192 −3 −198 6 24.926
111 144 156 4 −154 −154 2 158 −4 25.046
112 80 86 2 −85 −85 1 87 −2 25.342
113 16 16 0 −16 −16
0 16 0 25.639
114 −48 −54 −2 53 53 −1 −55 2 25.936
115 −112 −124 −4 122 122 −2 −126 4 26.232
116 209 227 6 −224 −224 3 230 −6 26.351
117 −176 −194 −6 191 191 −3 −197 6 26.529
118 145 157 4 −155 −155 2 159 −4 26.648
119 81 87 2 −86 −86 1 88 −2 26.945
120 17 17 0 −17 −17 0 17 0 27.241
121 −47 −53 −2 52 52 −1 −54 2 27.538
122 −111 −123 −4 121 121 −2 −125 4 27.835
123 210 228 6 −225 −225 3 231 −6 27.954
124 −175 −193 −6 190 190 −3 −196 6 28.131
125 146 158 4 −156 −156 2 160 −4 28.251
126 82 88 2 −87 −87 1 89 −2 28.547
127 18 18 0 −18 −18 0 18 0 28.844
128 −46 −52 −2 51 51 −1 −53 2 29.14
129 −110 −122 −4 120 120 −2 −124 4 29.437
130 211 229 6 −226 −226 3 232 −6 29.556
131 −174 −192 −6 189 189 −3 −195 6 29.734
132 147 159 4 −157 −157 2 161 −4 29.853
133 83 89 2 −88 −88 1 90 −2 30.15
134 19 19 0 −19 −19 0 19 0 30.446
135 −45 −51 −2 50 50 −1 −52 2
30.743
136 −109 −121 −4 119 119 −2 −123 4 31.04
137 212 230 6 −227 −227 3 233 −6 31.159
138 −173 −191 −6 188 188 −3 −194 6 31.336
139 148 160 4 −158 −158 2 162 −4 31.455
140 84 90 2 −89 −89 1 91 −2 31.752
141 20 20 0 −20 −20 0 20 0 32.049
142 −44 −50 −2 49 49 −1 −51 2 32.345
143 −108 −120 −4 118 118 −2 −122 4 32.642
144 213 231 6 −228 −228 3 234 −6 32.761
145 −172 −190 −6 187 187 −3 −193 6 32.939
146 149 161 4 −159 −159 2 163 −4 33.058
147 85 91 2 −90 −90 1 92 −2 33.355
148 21 21 0 −21 −21 0 21 0 33.651
149 −43 −49 −2 48 48 −1 −50 2 33.948
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M. Snyder / Natural Science 5 (2013) 963-971 967
Continued
150 −107 −119 −4 117 117 −2 −121 4 34.244
151 214 232 6 −229 −229 3 235 −6 34.364
152 −171 −189 −6 186 186 −3 −192 6 34.541
153 150 162 4 −160 −160 2 164 −4 34.66
154 86 92 2 −91 −91 1 93 −2 34.957
155 22 22 0 −22 −22 0 22 0 35.254
156 −42 −48 −2 47 47 −1 −49 2 35.55
157 −106 −118 −4 116 116 −2 −120 4 35.847
158 215 233 6 −230 −230 3 236 −6 35.966
159 −170 −188 −6 185 185 −3 −191 6 36.144
160 151 163 4 −161 −161 2 165 −4 36.263
161 87 93 2 −92 −92 1 94 −2 36.559
162 23 23 0 −23 −23 0 23 0 36.856
163 −41 −47 −2 46 46 −1 −48 2 37.153
164 −105 −117 −4 115 115 −2 −119 4 37.449
165 216 234 6 −231 −231 3 237 −6 37.569
166 −169 −187 −6 184 184 −3 −190 6 37.746
167 152 164 4 −162 −162 2 166 −4 37.865
168 88 94 2 −93 −93 1 95 −2 38.162
169 24 24 0 −24 −24 0 24 0 38.458
170 −40 −46 −2 45 45 −1 −47 2 38.755
171 −104 −116 −4 114 114 −2 −118 4 39.052
172 217 235 6 −232 −232 3 238 −6 39.171
173 −168 −186 −6 183 183 −3 −189 6 39.348
174 153 165 4 −163 −163 2 167 −4 39.468
175 89 95 2 −94 −94 1 96 −2 39.764
176 25 25 0 −25 −25 0 25 0 40.061
177 −39 −45 −2 44 44 −1 −46 2
40.358
178 −103 −115 −4 113 113 −2 −117 4 40.654
179 218 236 6 −233 −233 3 239 −6 40.773
180 −167 −185 −6 182 182 −3 −188 6 40.951
181 154 166 4 −164 −164 2 168 −4 41.07
182 90 96 2 −95 −95 1 97 −2 41.367
183 26 26 0 −26 −26 0 26 0 41.663
184 −38 −44 −2 43 43 −1 −45 2 41.96
185 −102 −114 −4 112 112 −2 −116 4 42.257
186 219 237 6 −234 −234 3 240 −6 42.376
187 −166 −184 −6 181
181 −3 −187 6 42.553
188 155 167 4 −165 −165 2 169 −4 42.672
189 91 97 2 −96 −96 1 98 −2 42.969
190 27 27 0 −27 −27 0 27 0 43.266
191 −37 −43 −2 42 42 −1 −44 2 43.562
192 −101 −113 −4 111 111 −2 −115 4 43.859
193 220 238 6 −235 −235 3 241 −6 43.978
194 −165 −183 −6 180 180 −3 −186 6 44.156
195 156 168 4 −166 −166 2 170 −4 44.275
196 92 98 2 −97 −97 1 99 −2 44.572
197 28 28 0 −28 −28 0 28 0 44.868
198 −36 −42 −2 41 41 −1 −43 2 45.165
199 −100 −112 −4 110 110 −2 −114 4 45.461
200 221 239 6 −236 −236 3 242 −6 45.581
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M. Snyder / Natural Science 5 (2013) 963-971
Copyright © 2013 SciRes.
968
Figures 1 and 2 should prove that the family of unitless
equations contained in Table 1 is not random but instead
is a structure made up of periodic waveforms.
use dimensional analysis to check that Eq.1 through
Eq.4 are unitless equations.

75
19
62 12 2
6
22
49 π5
π3
cF
AGNRw





 2
(1) 3. DISCUSSION
Once we know that the dimensionality of the left hand
sides of the equations are correct, then our focus switches
to the right hand side of the equations. One should note
by definition all the physical constants on the left hand
side are measurements and have limited accuracy.
2
113
255 7
6
2672 7
212
49 2
π5π
FRw
AGhN





 (2)

21
122
3222 72
3
234 22
492 5
π3
cF Rw
AGhN





 (3)

55 9
62
22
2
8
7
π54
π
27 3
chN
Rw
 
 
 

Obviously the equations based physical measurements
can not be more accurate than the measurements them-
selves. My method was to give the Maple software pro-
gram the benefit of the doubt when computing the right
hand sides of the equations.
9
(4) For example while factoring and processing Eq.3 with
Maple’s identify command, the Apery’s constant [9] ap-
pears in the result. Apery’s constant can be expressed as
a series, which means we could convert the right hand
side of Eq.3 into a series just by redistributing some of
the factors. For this reason I left Apery’s constant in the
answer which propagated to other the equations.
Figure 1 is a plot of Ta ble 1, and is intended to show
that the system of equations in Table 1 is not random but
very periodic. The green line represents the natural log of
the right hand sides of the equations and the other lines
represent the exponent powers of the physical constants.
I view the form of the right hand sides of the equations
as an idealized guess times an error term which was sup-
plied by the reduced row echelon operation.
Figure 2 is also a plot of Table 1, where the equations
of the table have been resorted based on the values of the
ninth column of the table, instead of the tenth column.
Figure 1. Plot of Table 1 sorted by the right hand side values.
OPEN ACCESS
M. Snyder / Natural Science 5 (2013) 963-971 969
Figure 2. Plot of Table 1 sorted by the exponent values of the Faraday constant term.
A problem is that the right hand side of the equations
are inherently more accurate than the left hand side of the
equations; which means any exact answer found by my
method is merely a good guess.
On the other hand, these guesses appear to have over
seven significant digits of accuracy. Practically speaking,
the right hand sides of Eq.1 through Eq.4 are close
enough to the “right answers” to solve most problems
and if one wishes more accuracy one can always use the
left hand side to directly compute a decimal value.
4. SUMMARY
In some ways, this paper is mundane. We have a fam-
ily of similar equations where any single equation can be
proven with dimensional analysis to be unitless.
Assuming that a suitable expression can be found for
the right hand sides of the equations, then most of these
equations could be used like a Swiss army knife to change
from one physical constant to another.
On the mundane side we basically have a relationship
between nine constants that connects the constants like a
key ring. On the other hand, one could argue that the
relationships shown in this paper existed before any of
the physical constants were measured.
Obviously I can not address the range of philosophical
issues that this paper may cause. To answer the reader’s
unspoken question, I do not know why these relation-
ships exist; I only know that each time that I check them
they seem to be correct. I invite other papers to address
the deeper issues and physical interpretations of my equa-
tions.
A database of over 17,000 equations is available for
download; the reader is encouraged to download the da-
tabase and verify my work. By definition the terms of
these equations tend to be self canceling, meaning if you
make the wrong substitution, the whole left hand side
can disappear and just leave a number. This has hap-
pened to me quite a few times in the last few months,
which leads me to my final statement of the paper: “I
claim nothing.”
REFERENCES
[1] Rømer, O. (1677) Lettre No 2104. In: J. Bosscha, Ed.,
Oeuvres Complètes de Christiaan Huygens, M. Nijhoff,
La Haye, 1888-1950.
[2] Planck, M. (1920) The genesis and present state of de-
velopment of the quantum theory. Nobel Lecture, El-
sevier Publishing, Amsterdam.
[3] Feynman, R., Leighton, R. and Sands, M. (1989) The
Feynman lectures on physics, vol. 1. Addison Wesley,
Boston, 35-2-35-3.
[4] Avogadro, A. (1811) Essai d’une maniere de determiner
Copyright © 2013 SciRes. OPEN ACCESS
M. Snyder / Natural Science 5 (2013) 963-971
970
les masses relatives des molecules elementaires des corps,
et les proportions selon lesquelles elles entrent dans ces
combinaisons. Journal de Physique, 73, 58-76.
[5] Newton, I. and Turnbull, H.W. (1960) The correspond-
dence of Isaac Newton: Volume 2 (1676-1687). Cam-
bridge University Press, Cambridge, 309.
[6] Maxwell, J.C. (1904) Treatise on electricity and magnet-
ism. Clarendon Press, Oxford, 173.
[7] Faraday, M. (1859) Experimental researches in chemistry
and Physics. Richard Taylor and William Francis, Cam-
bridge.
[8] Менделеев, Д.И. (1874) О сжимаемости газов (Из
лаборатории С.-Петербургского Университета). Жу-
рнал русского химического общ ес т ва и физического
общес т ва . Том 6, 309-352.
[9] Apéry, R. (1979) Irrationalité de ζ(2) et ζ(3). Astérisque,
61, 11-13.
Copyright © 2013 SciRes. OPEN ACCESS
M. Snyder / Natural Science 5 (2013) 963-971 971
APPENDIX I
----------------------------------------------------------------
#include "stdio.h"
#define searchsize 29
// Search Size Should be an Odd Interger Greater than 5
// nvcc helloworld08g29.cu -o world08g29 -arch=sm_21
-maxrregcount=24 -ccbin=gcc-4.4
// Note size 29 runs in about 15 seconds on a GTX560,
size 79 runs in a few hours.
// All rights reserved, M. Snyder June 18, 2013
// Looking for solutions of
(x4-x5)^2+(x3+x8)^2+(x4+x7+x8)^2+(x2+x4-x6)^2+(-2
*(x4+x6)+x8-x1-x2)^2+(2*(x2+x4)+x1+x5+3*x6)^2 = 0
__global__ void helloworld()
{
int x1,x2,x3,x4,x5,x6,x7,x8,rlow,rhgh;
rlow=-((gridDim.x-1)/2);
rhgh=((gridDim.x-1)/2);
x1=blockIdx.x+rlow;
x2=blockIdx.y+rlow;
x3=threadIdx.x+rlow;
x4=rlow;
x5=rlow;
x6=rlow;
x7=rlow;
x8=rlow;
while (x8<rhgh)
{
if (x4 + x7 == -x8){
if (x3 == -x8){
if ( (x2+x4) == x6){
if (2*(x2+x4) + x1 + x5 == -3*x6){
if (x4 == x5){
if (-2*( x4 + x6) + x8 == x1 + x2){
printf("%+4d,%+4d,%+4d,%+4d,%+4d,%+4d,%+4d,%+
4d \n", x1,x2,x3,x4,x5,x6,x7,x8);
}
}
}
}
}
}
x4=x4+1;
if (x4>rhgh){x5=x5+1;x4=rlow;
if (x5>rhgh){x6=x6+1;x5=rlow;
if (x6>rhgh){x7=x7+1;x6=rlow;
if (x7>rhgh){x8=x8+1;x7=rlow;
}
}
}
}
}
}
int main()
{
int rangeofsearch(searchsize),seconds;
dim3 grid,block;
grid.x=rangeofsearch;
grid.y=rangeofsearch;
block.x=rangeofsearch;
size_t buf=1e7;
cudaFuncSetCacheCon-
fig(helloworld,cudaFuncCachePreferL1);
cudaDeviceSetLimit(cudaLimitPrintfFifoSize, buf);
seconds = time(NULL);
helloworld<<<grid,block>>>();
cudaDeviceSynchronize();
printf ("\n\n\nComplete CUDA Time: %i ",
int(time(NULL))-seconds);
return 0;
----------------------------------------------------------------
APPENDIX II
A maple script one could use to check the program out-
put.
----------------------------------------------------------------
with(ScientificConstants);
c0 := evalf(Constant(c));
c0u := GetUnit(Constant(c));
h0 := evalf(Constant(Planck_constant));
h0u := GetUnit(Constant(Planck_constant));
G0 :=
evalf(Constant(Newtonian_constant_of_gravitation));
G0u := GetU-
nit(Constant(Newtonian_constant_of_gravitation));
w0 :=
evalf(Constant(Wien_displacement_law_constant));
w0u := GetU-
nit(Constant(Wien_displacement_law_constant));
R0 := evalf(Constant(R));
R0u := GetUnit(Constant(R));
N0 := evalf(Constant(Avogadro_constant));
N0u := GetUnit(Constant(Avogadro_constant));
A0 := 1;
A0u := Unit('A');
F0 := 96485.3399;
F0u := Unit('C')/Unit('mol');
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