The continent that saw the greatest increase in independent countries in the second half of the twentieth century was Africa. Here's why:
1. Decolonization Movement: During the mid-20th century, many African countries gained independence from European colonial powers. This period is often referred to as the decolonization movement.
2. Multiple Countries Gained Independence: Countries such as Ghana, Nigeria, Kenya, Tanzania, Algeria, and many others in Africa gained their independence from colonial rule during this time.
3. Increase in Sovereign Nations: The process of decolonization led to a significant increase in the number of sovereign nations in Africa, making it the continent with the greatest rise in independent countries during that period.
4. Political Shifts: The granting of independence to African nations marked a significant shift in global politics and the dismantling of colonial empires.
In conclusion, Africa experienced a substantial surge in the number of independent countries during the second half of the twentieth century due to the decolonization movement, leading to a significant political transformation on the continent.