# A Quick Intuition For Parametric Equations

Algebra is really about relationships. How are things connected? Do they move together, or apart, or maybe they’re completely independent?

This is a companion discussion topic for the original entry at http://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/

this is great - many thanks. could you do one on why 1 = 0.99999… ? I know this is a very taxing one for many.

Hi Dan, glad you liked it! That’s a great topic, I have an article on it here:

Instead of laying out a definitive answer, I prefer to think “Under what assumptions about numbers does 0.999… = 1?” and also “Are there any assumptions that could mean 0.999… is different from 1?”

when I teach scatter plots we often talk about underlying causation. Is x really correlated to y, or is something else causing that? – One I did was ice cream sales vs bee stings. – great post.

Thanks Hunter — funny how we thought of similar examples! (I guess ice cream represents summer for everyone.) x-y plots are a good example, just putting things on the same graph doesn’t mean one causes the other.

Hey Kalid, I appreciate the shout out in the article! I wanted to let you know that I created some real awesome investigative mathematical experiences for my students with the ideas we discussed over email. Just today we were looking for how to graph these kinds of functions as a class and the equations I wrote on the board the kids still refer to as “store sales,” “ice cream sales,” and “sunscreen sales” because it was such a great, concrete example for them to fall back on. This unit on Parametrics has been absolutely incredible and as an intern for teaching, that means the world to me (and the kids). I wish you the best!

Hi Seth, that’s so awesome to hear! Wow, I love the idea of kids learning a new analogy that sticks :). It’s really gratifying to hear when things are clicking in the actual classroom (vs. just ideas bouncing around in our heads), thanks for letting me know!

Hi Kalid,

Great article!

I am an epidemiologist and we try to find how certain factors affect outcomes.

But we need to control for certain confounding factors to find out if the factor is really a causal factor or if the relationship is confounded by another variable.

I think your insight can help epidemiologists and thus doctors and thus health!

Anyhow, it would be nice if you can somehow integrate your ideas with some medical problems that epidemiologists like me try to investigate.

Cheers.

[…] formal terms, we’ve introduced a new parameter to explain the interaction. To change a ratio from a/b to one parameterized by x, we can […]

I was looking at Ohm’S law where current is directly related to resistance but voltage is inversely related to resistance so what is the relationship between current and voltage?

Hi Omer, thanks for the suggestion, medical applications would be really fun :).

Basically, Ohm’s Law can be written V = IR

In this formulation, I see see “R” as the Oomph needed to push one charge through the system, and I as how frequently you wish to push charges through.

The amount of Voltage to create this scenario is V = IR. That is, if you double the voltage, you’ll double how many charges you can pull through in a given amount of time. R is the “difficulty” required to move a single unit charge through the system. The better the conductor, the easier it is (so the same Voltage can move more charges when pulling through metal wires, vs. wood, for example).

hi, great explanations!

I used your ice cream sunscreen idea with parametrics. Now I am wracking my brain for more ideas that have one independent and two dependent variables. It must be too late in the day…my brain is fried. Thanks for posting this…it has been integrated into my unit

@ Bill