I am following the Olympic diving.
I am always wondering why or how divers choose to jump from different positions on the platform (i.e not from the center)
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There is no rule governing where a diver should stand before diving. They can choose any place or position they like. According to the linked Wikipedia article on diving platform:
Diving platforms for FINA sanctioned meets must be at least 6 metres (20 ft) long and 2 metres (6.6 ft) wide.
The width is necessary because there is also a synchronized platform diving competition.