I am just curious about this, suppose I am an unschooled blind person who has no idea of any kind of geometrical concept in mind (such as angle, triangle, and so on).
And now I want to study a real value $t$ which satisfies the following equation $$a(t)^2+b(t)^2=1$$ With some luck, I can end up using the same notation like any non-blind person who have studied geometry by defining $$\sin(t)=a(t)$$ $$\,\cos(t)=b(t).$$ Starting from here, is there a way for me to keep going and develop the notion of $\pi$ purely algebraically?