Arithematic rules The primitive function $F(x)$ of $f(x)$ obeys the rule $F'(x)=f(x)$. With $F(x)$ the primitive of $f(x)$ holds for the definite integral. $$\int_a^b f(x)dx=F(b)-F(a)$$ If $u=f(x)$...

- Mathematics is the hammer that shatters the ice of our unconscious.
- Sometime around 2400 B.C., the ancient Sumerians noticed the apparent circular track of the Sun’s annual path across the sky and knew that it took about 360 days to complete the journey. Thus, it was reasonable for them to divide the circular path into 360 degrees to track the Sun’s daily movement. This eventually led to our modern 360-degree circle. I wonder whether modern scientists, with their metric systems, have considered replacing the ancient 360-degree circle with a 100- degree circle. In some sense, 360 degrees may be more useful than 100 degrees, simply because 360 has so many factors that provide a larger number of easily definable units: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, and 180. Of course, for real metric aficionados, there’s always the grad, which is defined such that there are 100 grads in a right angle. Thus, 1 degree equals 100/90 grads, and 400 grads correspond to a complete revolution around the circle. In the 1800s, the grad unit was introduced in France, where it is called the grade.