Write a report on inscribed square problem . 

Questions you need to answer in the report

• What makes some of the solved special cases simple? 
• What makes the unsolved special cases hard? 
• Are there any ’in-between’ special cases that have been solved, but whose proofs were very long and complicated?
• Please express your ideas in a precise and formal way, displaying clearly any relevant equations and labeled figure(s) that support your work, should they be relevant.
• please write it in your own words and also add the reference in it.