The golden ratio in the Quran - Spirituality Rekindled

Nassir H. Sabah

The golden ratio, recognized since about 300 BCE and referred to as the “divine proportion” is believed to be the basis of some of the most aesthetically pleasing and functional forms found in nature, art, and architecture.

A geometrical interpretation of the golden ratio is that it divides a straight line segment into two segments a and b, where a > b, such that a/b = (a +b)/a. In words, the golden ratio divides the straight line into two unequal segments such that the ratio of the length of the longer segment a to that of the shorter segment b is the same as the ratio of the total length of the line, (a + b), to the length of longer segment a. Multiplying out this equation and setting b equal to 1, gives a quadratic equation a² – a – 1 = 0. The golden ratio is the positive root of this equation and is equal to 1.618034, rounded to 7 significant figures.

The golden ratio, denoted by the Greek letter phi (φ), is an irrational number, like pi (π), which means that it cannot be expressed as the ratio of two integers. It should be noted that the digit sum of the 7-digit golden ratio 1.618034 is 23, which is the number of years over which the Quan was revealed and is also the number of chromosome pairs in humans. 7 is a mystical number that is the basis of many numerical relations and patterns in the Quran⁽¹⁾.

The golden ratio has some very interesting mathematical and geometrical derivatives and associations⁽²⁾, such as the Fibonacci and Lucas series of numbers, the golden triangle, the golden spiral, the golden angle, the pentagram, the octahedron, and many others.

In nature are found many structures that feature near-values of the golden ratio⁽³⁾. A striking universal example is in the dimensions of the DNA molecule, in which a complete cycle of its double helix spans 34 angstroms in length and 21 angstroms in width. These numbers follow the Fibonacci sequence (…, 13, 21, 34, …), which can be derived from the quadratic equation that defines the golden ratio⁽²⁾, with 34/21 = 1.6190. Other examples are the spiral patterns of sunflower seeds, pinecones, some seashells, hurricanes, galaxies, and proportions in human bodies, faces, limbs and fingers

In view of the importance of the golden ratio, it may be wondered whether the Quran, the word of Allāh (the proper name in Arabic of The One and Only God of the universe), makes any reference to the golden ratio. It does indeed, and in a manner that is characteristically objective and irrefutable. The Quran has 114 chapters and 6236 numbered verses. In the table below, the chapter numbers are entered in column (1) and the corresponding number of verses in each chapter is entered in column (2). The sum of the chapter number and the number of verses in the chapter is entered for each chapter in column (3). These sums are sorted in ascending order in column (4), from which it will be noted that some of these sums are repeated. The unrepeated sums are entered in column (5), whereas the repeated sums are entered in column (6). The entries in column (5) add to 4885, and those in column (6) add to 7906. The ratio 7906/4885 = 1.618424, which is within 0.0242% of the true value of the golden ratio.⁽⁴⁾

It may be argued that the choice of chapter numbers and numbers of verses in chapters is arbitrary and has fortuitously led to the near-value of the golden ratio. In fact, this is not the case. These numbers seem have special significance and are involved in other astounding numerical relations. For example, if the sums in column (3) of the table below are separated into odd and even numbers, instead of repeating and non-repeating numbers, the total of the odd numbers is 6555, the same as the sum of chapter numbers in column (1) of the table below, and the sum of the even numbers is 6236, the same as the count of the numbered verses in the Quran⁽⁵⁾, as in column (2) of the table below. Moreover, if the numbers of verses in each chapter that are prime numbers are added, their sum is 1076. If these prime numbers are considered prime order numbers instead of prime numbers, the corresponding prime numbers sum to 5160, where 1076 + 5160 = 6236, the same as the count of the numbered verses in the Quran⁽⁶⁾.

To remove any lingering doubt that the above reference to the golden ratio in the Quan is purely coincidental, consider that the 4 most significant digits, 1618, in both the true and calculated values of the golden ratio, refer to Chapter 16, Verse 18. This verse states: “And were you to count the blessings of Allāh, you could not number them. Truly Allāh is Ever-Forgiving, Ever-Merciful.” وَإِن تَعُدُّوا۟ نِعْمَةَ ٱللَّهِ لَا تُحْصُوهَآ ۗ إِنَّ ٱللَّهَ لَغَفُورٌ رَّحِيمٌ. Significantly, the verse consists of two separate sentences. The longer sentence in the Arabic verse consists of 24 letters and the shorter sentence consists of 15 letters. The ratios 24/15 and 39/24, corresponding to the ratios in the definition of the golden ratio, are 1.6 and 1.625, respectively. Their average, 1.6125, is within 0.343% of the true value of the golden ratio.

The number of words in the first sentence of Verse 16:18 is 6, not counting the conjunctive wāw as a separate letter, and the number of letters in the second sentence is 4. The two previously considered ratios are 6/4 = 1.5 and 10/6 = 1.666667, respectively, having an average of 1.583334, which is within 2.145% of the true value of the golden ratio. If the conjunctive wāw at the beginning of the first sentence is counted as a separate letter, as is sometimes done, the corresponding ratios are 7/4 = 1.75 and 11/7 = 1.571429, whose average, 1.660714, is within 2.638% of the true value of the golden ratio. The mean of the two averages, (1.660714 + 1.583334)/2 = 1.622024 is within 0.247% of the true value of the golden ratio.

The foregoing removes all reasonable doubt that the references to the golden ratio in the Quran are coincidental. So, how can the Quran be of other than divine origin?

(1) (2) (3) (4) (5) (6)

Number of chapters	Number of verses	Sum of first two columns	Third column in ascending order	Fourth column separated into repeating and nonrepeating numbers
1	7	8	8	8
2	286	288	56	56
3	200	203	62	62
4	176	180	65	65
5	120	125	66	66
6	165	171	67	67
7	206	213	73		73
8	75	83	73		73
9	129	138	74	74
10	109	119	75	75
11	123	134	77		77
12	111	123	77		77
13	43	56	78	78
14	52	66	80		80
15	99	114	80		80
16	128	144	81	81
17	111	128	82		82
18	110	128	82		82
19	98	117	83		83
20	135	155	83		83
21	112	133	85	85
22	78	100	86	86
23	118	141	88		88
24	64	88	88		88
25	77	102	90	90
26	227	253	93	93
27	93	120	95		95
28	88	116	95		95
29	69	98	95		95
30	60	90	97	97
31	34	65	98	98
32	30	62	99	99
33	73	106	100		100
34	54	88	100		100
35	45	80	101		101
36	83	119	101		101
37	182	219	102		102
38	88	126	102		102
39	75	114	102		102
40	85	125	103		103
41	54	95	103		103
42	53	95	103		103
43	89	132	104	104
44	59	103	106		106
45	37	82	106		106
46	35	81	106		106
47	38	85	106		106
48	29	77	106		106
49	18	67	107		107
50	45	95	107		107
51	60	111	107		107
52	49	101	109		109
53	62	115	109		109
54	55	109	110		110
55	78	133	110		110
56	96	152	110		110
57	29	86	110		110
58	22	80	110		110
59	24	83	111		111
60	13	73	111		111
61	14	75	111		111
62	11	73	112	112
63	11	74	113		113
64	18	82	113		113
65	12	77	113		113
66	12	78	114		114
67	30	97	114		114
68	52	120	114		114
69	52	121	114		114
70	44	114	114		114
71	28	99	115		115
72	28	100	115		115
73	20	93	115		115
74	56	130	115		115
75	40	115	116		116
76	31	107	116		116
77	50	127	116		116
78	40	118	117	117
79	46	125	118		118
80	42	122	118		118
81	29	110	119		119
82	19	101	119		119
83	36	119	119		119
84	25	109	119		119
85	22	107	120		120
86	17	103	120		120
87	19	106	120		120
88	26	114	121	121
89	30	119	122	122
90	20	110	123	123
91	15	106	125		125
92	21	113	125		125
93	11	104	125		125
94	8	102	126	126
95	8	103	127	127
96	19	115	128		128
97	5	102	128		128
98	8	106	130	130
99	8	107	132	132
100	11	111	133		133
101	11	112	133		133
102	8	110	134	134
103	3	106	138	138
104	9	113	141	141
105	5	110	144	144
106	4	110	152	152
107	7	114	155	155
108	3	111	171	171
109	6	115	180	180
110	3	113	203	203
111	5	116	213	213
112	4	116	219	219
113	5	118	253	253
114	6	120	288	288
6555	6236	12791	12791	4885	7906

References