Many years ago, I had read a book entitled "Think of a Number" by Malcolm E. Lines, and it was an eminently readable and thought provoking book. In the book, there were topics like Fibonacci numbers (along with the live examples from the nature) and Golden Section. Now I'm looking for a similar book. Can anyone recommend me one?
Another more general pop math book covering mathematical curiosities is Coincidences, Chaos, and All that Math Jazz. It is at the level you're talking about. A more focused book on the golden ratio is that by Mario Livio. One nice feature of this second book is that he does a nice job of pointing out places where people believe in coincidences that aren't really there. He stays nicely objective, where many others fail to.
I don't know the book you are speaking of, but for some reason I am reminded of 1089, and all that by David Acheson. This is a charming book about some mathematical curiosities and can be appreciated by the professional and enjoyed by the layperson.
The Number Devil may be something like what you're looking for.
Young Robert's dreams have taken a decided turn for the weird. Instead of falling down holes and such, he's visiting a bizarre magical land of number tricks with the number devil as his host. Starting at one and adding zero and all the rest of the numbers, Robert and the number devil use giant furry calculators, piles of coconuts, and endlessly scrolling paper to introduce basic concepts of numeracy, from interesting number sequences to exponents to matrices.
(It's not a watered-down kids' book, even though the description might suggest it.)
did you try the books of Eastaway and Wyndham? Why Do Buses Come in Threes? and How Long Is a Piece of String?
Blurb for the first one says "An amusing explanation of how maths is relevant to almost everything in life. Citing many examples of the way mathematics can explain common phenomena"; for the second, "This title is for anyone wanting to remind themselves - or discover for the first time - that maths is relevant to almost everything we do. Dating, cooking, travelling by car, gambling and ranking sportsmen all have links with intriguing mathematical problems that are explained in this book".