Comment by OpenPlex on 13/12/2023 at 20:02 UTC

1 upvotes, 2 direct replies (showing 2)

View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science

(asking at a high school level of general math but am exploring a bit deeper how equations work)

Canceling in equations:

When did canceling identical parts in opposite sides of equations start? What's the history, who first discovered it could be done?

Does It even matter where in the equation they are, or if they're doing totally different things, they'll cancel as long as they're present? (and you divide by their number)

People through history figuring out what some equation is revealing:

Saw a video[1] where they added the equations for gravitational force to f=ma, then they canceled the m on two sides, implying that mass accelerated by gravity doesn't matter, any amount of mass would experience the same amount of force.

1: https://m.youtube.com/watch?v=cPgXeeBmPNQ&t=420

In another video, a scientist whose equation resulted with a negative sign for the mass had interpreted that to imply the existence of antimatter.

Along those lines, what types of discoveries did people make in engineering, science, etc, from results of equations that unexpectedly implied a surprise or insight?

Replies

Comment by rmeredit at 13/12/2023 at 22:40 UTC

8 upvotes, 1 direct replies

This is probably more a question about the history of algebra than anything else, but it's worth pointing out that mathematical statements are just assertions of truth:

3 + 5 = 8

x +7 = y

When we make changes to an equation, like 'cancelling', or resolving for a given variable, we're making new statements of truth, justified by the previous statement being true, and adhering to the rules of logic when making the change.

That means, when we change, say 5+3 = 8 to 5 = 8-3 or even 8=8 (or 5 = 5), we're not just saying the same thing over and over, but making new statements that we're confident are true. 5=5 is different to saying 8=8, but we're confident both are true because of the original statement 5+3 = 8, and making sure that any adjustment we make to one side of an equation is balanced out by making the same on the other side.

The concept itself is intuitive enough that it probably pre-dates the idea of equations in the first place - kids understand it, say, when sharing things equally (if we have six things to share, we both start off with 0 and if give you three things, I need to give myself three things to even it out). Guaranteed the ancient Greeks understood it, and certainly the Persians understood it with the development of algebra.

Comment by flagstaff946 at 14/12/2023 at 04:00 UTC

0 upvotes, 1 direct replies

Many many many! One of the most incredible being the free space wave equation for light (and c^2 =(ue)^-1 )