Dear Scholar
1. We thought Square and Circle are different.
2. Archimedes did not calculate the area of the arbelos. He gave for it a formula. Why? Because , he himself did not know the EXACT Pi value. He simply said upper limit of Pi as 22/7. With that , only approximate area of circular constructions can be arrived at.
3. Golden Ratio , we thought , is nothing to do with circle and Pi. However, in recent days some mathematicians say Pi value as 3.144...based on Golden Ratio.
4.Surprisingly, with the revelation of the REAL PI VALUE called Cosmic Pi , by NATURE ,we come to know that so called above "UNRELATED GEOMETRICAL ENTITIES & CONCEPTS " are related and are unified as ONE.
Here is the attachment.