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Thanks for the clearer mathematical explanation by using correlation between amount of sides and amount of area. However, I am still chasing the logic, we can say the physical reason instead of the mathematical reason Are we losing area with smaller angles? Are small angles missing a smaller part of the area?

Imagine that you have a rope which is 24 cm long. If you make a perfect square from this rope (each side is 6 cm) then the area becomes 6 x 6 = 36 cm^2. If you make a perfect triangle (each side is 8 cm) from the same rope, then the area becomes (768)^0.5 which is approx. 28 cm^2 So the length of your border is always the same, but this same border length surrounds different amount of area for different shapes. The border length is the same, but the area size is different. I am not asking mathematical explanation, but I am searching for the logical explanation. What is the logic behind this? Difficult to understand the logic.

Yes swansont, you have right points. There are some animals which have natural tools on their body to protect and feed theirself, so there is no pressure on them to change theirself. Moreover, depth perception is very important for discovery. If I add a point, I think "having hands" is a very big advantage to be able to develop tools. According to the properties above, apes are very suitable to develop theirself. However, it is coming to same point again. Million years ago, humankind and many other ape kinds had similar brain, similar body properties and characteristics, similar living style, similar threats from other wild animals. What did push humankind to develop new tools and to discover new living tehcniques? Why didn't other apes feel the same pressure although we had similar life and threats?

Yes, I have seen documentaries which are showing that animals can learn some basic actions. However, I am asking same question again. Why did only humankind learn to learn? Why not other billions of animal kinds? What was the breaking point million years ago? How could we open our mind to learn new things? and Why couldn't other animals open their mind and they have kept their limited basic skills? Thanks, Gürol

Hello, My profession is not genetic, but I have a general knowledge on development of races and human evolution, so please forgive me if I write a wrong notation. According to the evolution theory, humanbeing was in same genetic family as all the ape kinds, we were one of the ape kinds with a primitive brain. Then for a reason, humanbeing developed his learning ability, developed shelters (like cave houses), hunting technics, cooking, discovered fire, new transportation technics, built up new human relationships, culture and civilizations. Finally we became superlative creatures in the planet. My question is "how" or "why" humanbeing developed his learning ability altough all the other ape kinds have kept their primitive brains? If you answer like "There was a threat to humankind, so they developed this skill with his surviving instinct", then I will ask you back like "Then there must be similar threats to other apes too, and there has been hundreds of different ape types, many of them had a very similar brain structure to human brain structure. Why didn't any of these ape kinds develope its learning skills?" Thanks, Gürol