Complementary view of 18 and 57
This is the second pair of chps that possess the unique property that the number of verses between them is encoded in their individual verses (pointed by the curved arrows), similar to the pair 29 and 84 here. The curved arrows emphasize the relationship between chp 64 with its 18 verses, and 57 with its 29 verses. Chp 57 is also of ord 29 (the double-arrow) (see Glossary). As we can see in the diagram, the two cases look quite similar. Except for the double-arrow, the two Fig's look almost identical in both cases. There are five nodes (chps) participating in both Fig's which are related to each other via their ords. Chp 29 is of ord 15, which itself along with 18 are both of ord 9. If we write 2964 = 57 × 52, we can see how 52 relates to 18 via its 49 verses, which itself has 18 verses - back to the 18 and 57 pair! The total norm at the end of chp 57 is 2449. This points to 18 again through chp 24 which has 64 verses, which itself has 18 verses. Furthermore, the norm from 18 to 64 is 1019, pointing to chp 19 with ord 10. Also from 29 to 64 there are 513 = 19 × 27 GV's. Now, 64th ord is 93, which is the verses of chp 27!
Chp 57 is called "The Iron", and the name of the chp appears in 57:25, where we are reminded that it was sent down wherein there's strength and many benefits for the people. This is the 19th GV in this chp and the relative norm up to this verse is 26 which is also the atomic number (A-number) of iron! It is noteworthy that a total of three metals are mentioned in the book; iron, silver and gold. Their A-numbers 26, 47, 79 respectively, add up to 152 = 19 × 8.
The total norm up to 57:25 is 2443, where we see the connection to chp 43 with ord 24, which itself is of ord 13 - the digit-sum of 2443, and an indirect reference to chp 13 and its 43 verses. Now, 26 × 57 = 1482, which is the total ALMR count in chp 13! Additionally, 1482 has an interesting property of its own relating 14 to 82: chp 82 is of ord 53, which is of ord 25, which itself is of ord 14! We notice that 25 appears in this sequence too. At the end of chp 57 there are 1665 = 45 × 37 GV's. Here we see the relationship between 45 and its 37 verses plus the fact that 45 itself is of ord 26 and 37 is of ord 18! The sum of the GV's up to 57:25 is 116392. Here, we see another interesting property: 92 is of ord 63, which itself has 11 verses! The sum of its digits is 22, and chp 22 is the 11th ord!
Chp 18 has 14 GV's. The last one is verse 69. This is also the verses of 29 which itself is the verses of 57. The total norm at 18:69 is 1599. This again is a reference to 15 and its 99 verses, and 29 itself is the 15th ord. This relationship between 18 and 29 goes even further as follows. There are 24 EC's from 18 to 64 with a total number of 1587 verses, which can be taken as a hint at the verse 15:87 referring to the "seven pairs". And finally, we notice that 57 ± 18 = 75, 39, an indirect reference to chp 39 and its 75 verses.