Text: prime factorization of 18:

Correct capitalization: Prime factorization of 18:

Text: although his research was in applied mathematics, it was through the problem of accretion of gas by a large gravitating body which ray lyttleton discussed with him that hoyle's interests turned towards mathematical problems in astronomy.

Correct capitalization: Although his research was in applied mathematics, it was through the problem of accretion of gas by a large gravitating body which Ray Lyttleton discussed with him that Hoyle's interests turned towards mathematical problems in astronomy.

Text: after a smoke on the deck we dive into a siesta. a bit of solitude and peace is nice when you are with other people constantly.

Correct capitalization: After a smoke on the deck we dive into a siesta. A bit of solitude and peace is nice when you are with other people constantly.

Text: theme parks, spas and much, much more.

Correct capitalization:
Theme parks, spas and much, much more.