The book is thinking of the five rings joined together into one symbol. The cloth is a flag. The colours don't represent individual continents:
As can be read in the Olympic Charter, the Olympic symbol represents the union of the five continents and the meeting of athletes from throughout the world at the Olympic Games. However, no continent is represented by any specific ring. Though colourful explanations about the symbolism of the coloured rings exist, the only connection between the rings and the continents is that the number five refers to the number of continents.
Olympic symbols - Wikipedia, the free encyclopedia
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