The story of the Oscar-nominated movie, "Hidden Figures," revolves around the female African-American mathematicians and the 'ancient' mathematical method which made NASA's space missions successful.
Katherine Johnson, Mary Vaughan, and Mary Jackson were working as human computers at NASA calculating complex mathematical equations by hand. Despite their brilliance, these women were looked down because of their gender and color. But as fate would have it, they would go down in history as one of the heroes that made America's space dream a reality.
That brilliance became evident when scientists at NASA kept getting stumped from finding the right equation to a successful trajectory. In one scene of the movie, the engineers were discussing about the problem until Johnson stepped in and suggest they try the Euler's method. However, the other scientists were wary about using it and referred to it as being 'ancient.'
What is Euler's method and was it really used to successfully made John Glenn the first man to orbit the Earth?
Euler'e method can be considered 'ancient' since Swiss mathematician Leonhard Euler developed it a long time ago before his death in 1783. It's an approximation technique used to solve a differential equation.
When using the method, three things should be present - the starting point, information to the step size or information how to find the step size, and the differential equation. It uses the concept of local linearity to put together a series of small line segments so that an approximation of the actual curve can be made. Therefore, every time this method is used, one point is created to form another line segment.
Euler's method becomes much more effective if the points are closer to each other and the changes in the solution is slow and smooth because there are errors that can occur in each step of the process.
Now, did Johnson really use this method?
In a technical report Johnson co-authored with NASA engineer Ted Skopinski, they described the the calculations they did as they analyzed the trajectories. However, they did not solely used Euler's method to calculate these differential equations but drew upon a number of branches of math. Even then, this 'ancient' method is indeed beautiful and not ancient at all.
