Thenumberswhicharedivisiblebythree Thenumberswhicharedivisiblebythree Thenumberswhicharedivisiblebythree three In this section we will first determine the numbers which are contained in the index of Qur’ān that are divided by three. Then,wewillinvestigatewhetheramathematicalharmonyexists betweenthemornot. Inthefollowinglist,thenumberscontainedintheindexof Qur’ānwhicharedivisiblebythreearemarked: No. Surah Ayat No. Surah Ayat Ayat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Al-Fāti&a Al-Baqarah Āl‘Imrān Al-Nisā Al-Māidah Al-En‘ām Al-A‘rāf Al-Anfāl Al-Tawbah Yūnus Hūd Yūsuf Al-Ra‘d Ibrāhīm Al-1ijr Al-Na&l Al-’Isrā Al-Kahf Maryam ;āhā Al-Anbiyā Al-1ajj Al-Mu’minūn Al-Nūr 7 286 200 176 120 165 206 75 129 109 123 111 43 52 99 128 111 110 98 135 112 78 118 64 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 Al-Mujādalah Al-1ashr Al-Mumta&inah Al-7aff Al-Jumu‘ah Al-Munāfiqūn Al-Taghābun Al-;alāq Al-Ta&rīm Al-Mulk Al-Qalam Al-1āqqah Al-Ma‘ārij Nū& Al-Jinn Al-Muzzammil Al-Muddaththir Al-Qiyāmah Al-Insān Al-Mursalāt Al-Naba’ Al-Nāzi‘āt ‘Abasa Al-Takwīr 22 24 13 14 11 11 18 12 12 30 52 52 44 28 28 20 56 40 31 50 40 46 42 29 185 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com 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 Al-Furqān Al-Shu‘arā Al-Naml Al-QaCaC Al-‘Ankabūt Al-Rūm Luqmān Al-Sajdah Al-A&zāb Saba FāBir Yāsīn Al-7affāt 7ād Al-Zumar Al-Mu’min FuCCilat Al-Shūrā Al-Zukhruf Al-Dukhān Al-Jāthiyah Al-A&qāf Mu&ammad Al-Fat& Al-1ujurāt Qāf Al-Dhāriyāt Al-;ūr Al-Najm Al-Qamar Al-Ra&mān Al-Wāqi‘ah Al-1adīd 77 227 93 88 69 60 34 30 73 54 45 83 182 88 75 85 54 53 89 59 37 35 38 29 18 45 60 49 62 55 78 96 29 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 List-90 186 Al-InfiBār Al-MuBaffifīn Al-Inshiqāq Al-Burūj Al-;āriq Al-A‘lā Al-Ghāshiyah Al-Fajr Al-Balad Al-Shams Al-Layl Al-Fu&a Al-Inshirā& Al-Tīn Al-‘Alaq Al-Qadr Al-Bayyinah Al-Zilzāl Al-‘Ādiyāt Al-Qāri‘ah Al-Takāthur Al-‘Asr Al-Humaza Al-Fīl Quraysh Al-Mā‘ūn Al-Kawthar Al-Kāfirūn Al-NaCr Tabbat Al-IkhlāC Al-Falaq Al-Nās 19 36 25 22 17 19 26 30 20 15 21 11 8 8 19 5 8 8 11 11 8 3 9 5 4 7 3 6 3 5 4 5 6 Thenumberswhicharedivisiblebythree LetusnowdividethenumbersintheindexofQur’āninto two categories of homogeneous and non-homogeneous, with respectto“divisiblebythree”. Example for the surahs with homogeneous sequence numbersandnumberofayats: 6 Al-En‘ām 165 Al-En‘ām is a homogeneous surah. Forwhy, both the sequencenumberandthenumberofayats,meettheconditionof “divisiblebythree”.Therefore,al-En‘āmsurahishomogeneousin thisrespect. 1 Al-Fāti&a 7 Surah al-Fāti&a is also a homogeneous surah. Forwhy, neitherthesequencenorthenumberofayats,meetsthecondition of“divisiblebythree”.Therefore,al-Fāti&asurahishomogeneous inthisrespect. Exampleforthesurahsofwhichtheirsequencenumbers andnumberofayatsarenothomogeneous: 18 Al-Kahf 110 The sequence number of al-Kahf surah meets the conditionof“divisiblebythree”,whereasit’snumberofayatsdoes not cover this condition. Therefore, al-Kahf surah is not homogeneousinthisrespect. 5 Al-Māidah 120 The number of ayats of al-Māidah surah meets the condition of “divisible by three”, whereas it’s sequence number does not cover this condition. Therefore, al-Māidah surah is not homogeneousinthisrespect. 187 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com Thesetofsurahswhicharehomogeneouswithregardto hesetofsurahswhicharehomogeneouswithregardto “divisiblebythree”ofthesequencenumbersandthe divisiblebythree”ofthesequencenumbersandthe numberofayats. numberofayats. No. Surah 1 2 4 6 7 9 10 12 Al-Fāti&a Al-Baqarah Al-Nisā Al-En‘ām Al-A‘rāf Al-Tawbah Yūnus Yūsuf 13 14 15 16 19 23 25 26 27 28 30 31 37 38 39 40 43 44 46 47 188 Al-Ra‘d Ibrāhīm Al-1ijr Al-Na&l Maryam Al-Mu’minūn Al-Furqān Al-Shu‘arā Al-Naml Al-QaCaC Al-Rūm Luqmān Al-7affāt 7ād Al-Zumar Al-Mu’min Al-Zukhruf Al-Dukhān Al-A&qāf Mu&ammad XXX Ayat No. 7 286 176 165 206 129 109 111 53 58 61 62 66 68 70 71 43 73 52 99 128 98 118 77 227 93 88 60 34 182 88 75 85 89 59 35 38 74 76 77 79 82 85 86 88 94 95 97 98 100 101 106 107 108 112 113 Surah Ayat Ayat Al-Najm Al-Mujādalah Al-7aff Al-Jumu‘ah Al-Ta&rīm Al-Qalam Al-Ma‘ārij Nū& AlMuzzammil AlMuddaththir Al-Insān Al-Mursalāt Al-Nāzi‘āt Al-InfiBār Al-Burūj Al-;āriq Al-Ghāshiyah Al-Inshirā& Al-Tīn Al-Qadr Al-Bayyinah Al-‘Ādiyāt Al-Qāri‘ah Quraysh Al-Mā‘ūn Al-Kawthar Al-IkhlāC Al-Falaq 62 22 14 11 12 52 44 28 20 56 31 50 46 19 22 17 26 8 8 5 8 11 11 4 7 3 4 5 Thenumberswhicharedivisiblebythree 51 52 Al-Dhāriyāt Al-;ūr 60 49 114 6 Al-Nās List-91 Thereare59 59surahsinList-91 59 Let’shavealookathowmanyofthesesurahstakeplacein the first half and how many ofthem are contained in the second halfoftheHolyQur’ān: ThesurahsexistinthefirsthalfoftheHolyQur’ānand ThesurahsexistinthefirsthalfoftheHolyQur’ānand Qur’ānand whicharehomogeneouswithregardto“divisibleby divisibleby whicharehomogeneouswithregardto“ three”ofthesequencenumbersandthenumberof three”ofthesequencenumbersandthenumberof ayats. ayats. No. Surah Ayat No. Surah Ayat Ayat 1 2 4 6 7 9 10 12 13 14 15 16 19 23 25 26 Al-Fāti&a Al-Baqarah Al-Nisā Al-En‘ām Al-A‘rāf Al-Tawbah Yūnus Yūsuf Al-Ra‘d Ibrāhīm Al-1ijr Al-Na&l Maryam Al-Mu’minūn Al-Furqān Al-Shu‘arā 7 286 176 165 206 129 109 111 43 52 99 128 98 118 77 227 27 28 30 31 37 38 39 40 43 44 46 47 51 52 53 Al-Naml Al-QaCaC Al-Rūm Luqmān Al-7affāt 7ād Al-Zumar Al-Mu’min Al-Zukhruf Al-Dukhān Al-A&qāf Mu&ammad Al-Dhāriyāt Al-;ūr Al-Najm 93 88 60 34 182 88 75 85 89 59 35 38 60 49 62 List-92 Thereare31 31surahsinList-92 31 31isaprimenumber! 31 189 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com Thesurahsexistinthesecond ThesurahsexistinthesecondhalfoftheHoly secondhalfoftheHolyQur’ān halfoftheHolyQur’ān andwhicharehomogeneouswithregardto“ andwhicharehomogeneouswithregardto“divisibleby whicharehomogeneouswithregardto“divisibleby three”ofthesequencenumbersandthenumberof three”ofthesequencenumbersandthenumberof ayats. ayats. No. Surah Ayat No. Surah Ayat Ayat 58 61 62 66 68 70 71 73 74 76 77 79 82 85 Al-Mujādalah Al-7aff Al-Jumu‘ah Al-Ta&rīm Al-Qalam Al-Ma‘ārij Nū& Al-Muzzammil Al-Muddaththir Al-Insān Al-Mursalāt Al-Nāzi‘āt Al-InfiBār Al-Burūj 22 14 11 12 52 44 28 20 56 31 50 46 19 22 86 88 94 95 97 98 100 101 106 107 108 112 113 114 Al-;āriq Al-Ghāshiyah Al-Inshirā& Al-Tīn Al-Qadr Al-Bayyinah Al-‘Ādiyāt Al-Qāri‘ah Quraysh Al-Mā‘ūn Al-Kawthar Al-IkhlāC Al-Falaq Al-Nās 17 26 8 8 5 8 11 11 4 7 3 4 5 6 List-93 Thereare28 28surahsinList-93 28 28isnotaprimenumber! 28 190 Thenumberswhicharedivisiblebythree Homogenoussurahs 59 28 31 Thenumberof homogenoussurahs whichareincluded inthefirsthalfof theHolyQur'ān Thenumberof homogenoussurahs whichareincludedin thesecondhalfofthe HolyQur'ān Figure-18Distributionofthehomogeneoussurahs(asprimeandnon-prime)is shown. Evaluation The surahs which are homogeneous with regard to “divisible by three” of the sequence numbers and the number of ayats are distributed as (prime and nonprime) numbers in the first and second half of Qur’an. What about the non-homogeneous surahs? Now,let’sexaminethenon-homogeneoussurahswiththe sameapproach. Thesetofsurahswhicharenon hesetofsurahswhicharenonnon-homogeneouswith homogeneouswith regardto“divisiblebythree regardto“divisiblebythree”ofthesequencenumbers divisiblebythree”ofthesequencenumbers andthenumberofayats. andthenumberofayats. No. Surah Ayat No. Surah Ayat Ayat 3 5 8 11 17 Āl‘Imrān Al-Māidah Al-Anfāl Hūd Al-’Isrā 200 120 75 123 111 63 64 65 67 69 Al-Munāfiqūn Al-Taghābun Al-;alāq Al-Mulk Al-1āqqah 11 18 12 30 52 191 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com 18 20 21 22 24 29 32 33 34 35 36 41 42 45 48 49 50 54 55 56 57 59 60 Al-Kahf ;āhā Al-Anbiyā Al-1ajj Al-Nūr Al-‘Ankabūt Al-Sajdah Al-A&zāb Saba FāBir Yāsīn FuCCilat Al-Shūrā Al-Jāthiyah Al-Fat& Al-1ujurāt Qāf Al-Qamar Al-Ra&mān Al-Wāqi‘ah Al-1adīd Al-1ashr Al-Mumta&inah 110 135 112 78 64 69 30 73 54 45 83 54 53 37 29 18 45 55 78 96 29 24 13 72 75 78 80 81 83 84 87 89 90 91 92 93 96 99 102 103 104 105 109 110 111 28 40 40 42 29 36 25 19 30 20 15 21 11 19 8 8 3 9 5 6 3 5 Al-Jinn Al-Qiyāmah Al-Naba’ ‘Abasa Al-Takwīr Al-MuBaffifīn Al-Inshiqāq Al-A‘lā Al-Fajr Al-Balad Al-Shams Al-Layl Al-Fu&a Al-‘Alaq Al-Zilzāl Al-Takāthur Al-‘Asr Al-Humaza Al-Fīl Al-Kāfirūn Al-NaCr Tabbat List-94 Thereare55 55surahsinList-94 55 Let’shavealookathowmanyofthesesurahstakeplacein the first half and how many ofthem are contained in the second halfoftheHolyQur’ān: Thesurahswhicharecontainedinthefirsthalfofthe Qur’ān,andregar ,andregardedasnon Qur’ān ,andregardedasnondedasnon-homogeneouswithrespect homogeneouswithrespect to“divisiblebythree to“divisiblebythree”ofthesequencenumbersandthe divisiblebythree”ofthesequencenumbersandthe numberofayats: numberofayats: 192 Thenumberswhicharedivisiblebythree No. Surah Ayat No. Surah Ayat Ayat 3 5 8 11 17 18 20 21 22 24 29 32 33 Āl‘Imrān Al-Māidah Al-Anfāl Hūd Al-’Isrā Al-Kahf ;āhā Al-Anbiyā Al-1ajj Al-Nūr Al-‘Ankabūt Al-Sajdah Al-A&zāb 200 120 75 123 111 110 135 112 78 64 69 30 73 34 35 36 41 42 45 48 49 50 54 55 56 57 Saba FāBir Yāsīn FuCCilat Al-Shūrā Al-Jāthiyah Al-Fat& Al-1ujurāt Qāf Al-Qamar Al-Ra&mān Al-Wāqi‘ah Al-1adīd 54 45 83 54 53 37 29 18 45 55 78 96 29 List-95 Thereare26 26surahsinList-95 26 26isnotaprimenumber! 26 Thesurahswhicharecontainedinthesecond Thesurahswhicharecontainedinthesecondhalfofthe secondhalfofthe Qur’ān,andregardedasnon Qur’ān,andregardedasnon,andregardedasnon-homogeneouswithrespect homogeneouswithrespect to“divisiblebythree to“divisiblebythree”ofthesequ ”ofthesequencenumbersandthe divisiblebythree”ofthesequencenumbersandthe numberofayats: numberofayats: No. Surah Ayat No. Surah Ayat Ayat 59 60 63 64 65 67 69 72 75 Al-1ashr Al-Mumta&inah Al-Munāfiqūn Al-Taghābun Al-;alāq Al-Mulk Al-1āqqah Al-Jinn Al-Qiyāmah 24 13 11 18 12 30 52 28 40 89 90 91 92 93 96 99 102 103 Al-Fajr Al-Balad Al-Shams Al-Layl Al-Fu&a Al-‘Alaq Al-Zilzāl Al-Takāthur Al-‘Asr 30 20 15 21 11 19 8 8 3 193 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com Al-Naba’ ‘Abasa Al-Takwīr Al-MuBaffifīn Al-Inshiqāq Al-A‘lā 78 80 81 83 84 87 40 42 29 36 25 19 104 105 109 110 111 9 5 6 3 5 Al-Humaza Al-Fīl Al-Kāfirūn Al-NaCr Tabbat List-96 Thereare29 29surahsinList-96 29 29isaprimenumber! 29 Non-homogenoussurahs 55 26 Thenumberofnonhomogeneous surahswhichare includedinthefirst halfoftheHoly Qur'ān 29 Thenumberofnonhomogenoussurahs whichareincludedin thesecondhalfofthe HolyQur'ān Figure-19Distributionofthenon-homogeneoussurahs(asprimeandnonprime)isshown. Evaluation Evaluation The surahs which are not homogeneous with regard to “divisible by three” of the sequence numbers and the number of ayats are also distributed as (prime and non-prime) numbers in the first and second half of Qur’an. Let’sseetheresultswhichoutcomecollectively: 194 Thenumberswhicharedivisiblebythree NO. SURAH AYAT HOMOGENOUS 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 Al-Fātiḥa Al-Baqarah Āl ‘Imrān Al-Nisā Al-Māidah Al-En‘ām Al-A‘rāf Al-Anfāl Al-Tawbah Yūnus Hūd Yūsuf Al-Ra‘d Ibrāhīm Al-Ḥijr Al-Naḥl Al-’Isrā Al-Kahf Maryam Ṭāhā Al-Anbiyā Al-Ḥajj Al-Mu’minūn Al-Nūr Al-Furqān Al-Shu‘arā Al-Naml Al-Qaṣaṣ Al-‘Ankabūt Al-Rūm Luqmān Al-Sajdah Al-Aḥzāb Saba Fāṭir Yāsīn Al-Ṣaffāt Ṣād Al-Zumar Al-Mu’min Fuṣṣilat Al-Shūrā Al-Zukhruf Al-Dukhān Al-Jāthiyah Al-Aḥqāf Muḥammad Al-Fatḥ Al-Ḥujurāt Qāf Al-Dhāriyāt Al-Ṭūr Al-Najm Al-Qamar Al-Raḥmān Al-W āqi‘ah Al-Ḥadīd 7 286 200 176 120 165 206 75 129 109 123 111 43 52 99 128 111 110 98 135 112 78 118 64 77 227 93 88 69 60 34 30 73 54 45 83 182 88 75 85 54 53 89 59 37 35 38 29 18 45 60 49 62 55 78 96 29 X X 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 Al-Mujādalah Al-Ḥashr Al-Mumtaḥinah Al-Ṣaff Al-Jumu‘ah Al-Munāfiqūn Al-Taghābun Al-Ṭalāq Al-Taḥrīm Al-Mulk Al-Qalam Al-Ḥāqqah Al-Ma‘ārij Nūḥ Al-Jinn Al-Muzzammil Al-Muddaththir Al-Qiyāmah Al-Insān Al-Mursalāt A l - N a b a’ Al-Nāzi‘āt ‘A b a s a Al-Takwīr Al-Infiṭār Al-Muṭaffifīn Al-Inshiqāq Al-Burūj Al-Ṭāriq Al-A‘lā Al-Ghāshiyah Al-Fajr Al-Balad Al-Shams Al-Layl Al-Ḍuḥa Al-Inshirāḥ Al-Tīn Al-‘Alaq Al-Qadr Al-Bayyinah Al-Z ilzāl Al-‘Ādiyāt A l - Q ā r i ‘a h Al-Takāthur A l - ‘A s r Al-Humaza Al-Fīl Quraysh Al-Mā‘ūn Al-Kawthar Al-Kāfirūn Al-Naṣr Tabbat Al-Ikhlāṣ Al-Falaq A l - N ā s 22 24 13 14 11 11 18 12 12 30 52 52 44 28 28 20 56 40 31 50 40 46 42 29 19 36 25 22 17 19 26 30 20 15 21 11 8 8 19 5 8 8 11 11 8 3 9 5 4 7 3 6 3 5 4 5 6 NON-HOMOGENOUS X X X X X X X X X X X X X X X X X 31 26 X X X X X X X X X X X X X X X X X X X X X X X X X s y m m e t r y X X X o f o f a x i s a x i s s y m m e t r y X X X X X X X X X X a x i s o f s y m m e t r y X X X X X X X X X X X X X X X X X X X 28 29 X X X X X X X X X X X X X X X X In the figure, symmetric distribution of the homogenous and non-homogenous surahs to the first and second half of the Qur'an is shown. X X X X X X X X X X X X X X X X X X X X X X 195 BinarySymmetricBook dr.eng.halisaydemir www.symmetricbook.com NO. SURAH AYAT HOMOGENOUS 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 Al-Fātiḥa Al-Baqarah Āl ‘Imrān Al-Nisā Al-Māidah Al-En‘ām Al-A‘rāf Al-Anfāl Al-Tawbah Yūnus Hūd Yūsuf Al-Ra‘d Ibrāhīm Al-Ḥijr Al-Naḥl Al-’Isrā Al-Kahf Maryam Ṭāhā Al-Anbiyā Al-Ḥajj Al-Mu’minūn Al-Nūr Al-Furqān Al-Shu‘arā Al-Naml Al-Qaṣaṣ Al-‘Ankabūt Al-Rūm Luqmān Al-Sajdah Al-Aḥzāb Saba Fāṭir Yāsīn Al-Ṣaffāt Ṣād Al-Zumar Al-Mu’min Fuṣṣilat Al-Shūrā Al-Zukhruf Al-Dukhān Al-Jāthiyah Al-Aḥqāf Muḥammad Al-Fatḥ Al-Ḥujurāt Qāf Al-Dhāriyāt Al-Ṭūr Al-Najm Al-Qamar Al-Raḥmān Al-W āqi‘ah Al-Ḥadīd 7 286 200 176 120 165 206 75 129 109 123 111 43 52 99 128 111 110 98 135 112 78 118 64 77 227 93 88 69 60 34 30 73 54 45 83 182 88 75 85 54 53 89 59 37 35 38 29 18 45 60 49 62 55 78 96 29 X X 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 Al-Mujādalah Al-Ḥashr Al-Mumtaḥinah Al-Ṣaff Al-Jumu‘ah Al-Munāfiqūn Al-Taghābun Al-Ṭalāq Al-Taḥrīm Al-Mulk Al-Qalam Al-Ḥāqqah Al-Ma‘ārij Nūḥ Al-Jinn Al-Muzzammil Al-Muddaththir Al-Qiyāmah Al-Insān Al-Mursalāt A l - N a b a’ Al-Nāzi‘āt ‘A b a s a Al-Takwīr Al-Infiṭār Al-Muṭaffifīn Al-Inshiqāq Al-Burūj Al-Ṭāriq Al-A‘lā Al-Ghāshiyah Al-Fajr Al-Balad Al-Shams Al-Layl Al-Ḍuḥa Al-Inshirāḥ Al-Tīn Al-‘Alaq Al-Qadr Al-Bayyinah Al-Z ilzāl Al-‘Ādiyāt A l - Q ā r i ‘a h Al-Takāthur A l - ‘A s r Al-Humaza Al-Fīl Quraysh Al-Mā‘ūn Al-Kawthar Al-Kāfirūn Al-Naṣr Tabbat Al-Ikhlāṣ Al-Falaq A l - N ā s 22 24 13 14 11 11 18 12 12 30 52 52 44 28 28 20 56 40 31 50 40 46 42 29 19 36 25 22 17 19 26 30 20 15 21 11 8 8 19 5 8 8 11 11 8 3 9 5 4 7 3 6 3 5 4 5 6 non-prime X X X X X prime X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X a x i s o f s y m m e t r y X X X X X prime non-prime X X s y m m e t r y s y m m e t r y X o f o f X X X a x i s X X X X X X X X X X X X X X X X X X In the figure, symmetric distribution of the homogenous and non-homogenous surahs to the first and second half of the Qur'an is shown. X X X a x i s 196 NON-HOMOGENOUS X X X X X X X X X
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