Interesting. I do not remember pondering 1 ÷ 3 before having 3 to infinity, even though is 1/3. I will ponder more. I always ponder the number 6. It is the first perfect number in mathematics. It is followed by 28, 496, 8128, and so forth. There are 48 known perfect numbers today.
Even though I know not much of its meaning with mathematics or else, I enjoyed reading how it is obtained and its use.
Quoting one source "Despite the fact that Nicomachus offered no justification of his assertions, they were taken as fact for many years. Of course there was the religious significance that we have not mentioned yet, namely that 6 is the number of days taken by God to create the world, and it was believed that the number was chosen by him because it was perfect. Again God chose the next perfect number 28 for the number of days it takes the Moon to travel round the Earth. Saint Augustine (354-430) writes in his famous text The City of God :-
Six is a number perfect in itself, and not because God created all things in six days; rather, the converse is true. God created all things in six days because the number is perfect... "
Another perspective to consider is a circle can be constructed around a triangle and within a triangle for infinity as the triangle is reconstructed with the same rules with difference in size only or not.