We can imagine a point P on a circle, and Pθ is a point obtained from P by rotating it around the circle by angle θ counterclockwise. Assume T(θ) is the temperature at Pθ, and T(θ) is continuous from 0 to 2π (which also included 0 and 2π), and T(0) equals T(2π). Then assume another function f(θ)= T(θ) − T(θ + π). If values of θ are from 0 to π, so f(θ) is the temperature’s differences of two opposite points P and Pθ. Now we have two possibilities, if f(0) equals 0, then f(0) equals f(θ) equals 0. But if f(0) is not equal to 0, then f(p)=T(π)-T(2π). As we mentioned before, T(0) equals to T(2π). So, f(π)=T(π)-T(0). We can also write as f(π)=-(T(0)-T(π)) which is –f(0). Therefore, if f(π) is positive, then f(0) is negative (vise versa). By the Intermediate Value Theorem, if there is a point c larger than zero but smaller than π, then f(0) equals to zero. Therefore, T(c)=T(c+π). C and C+π have the same temperature but opposite positions. We can also imagine these two points are two countries on the earth. We know the countries locate on the equator of earth has the highest temperature. Earth is a kind of sphere, countries are on the equator have the same temperature but can be the opposite to each other.