3 ms·

The triangle, or “delta”, is used to indicate a tiny change in the following variable. Let’s say you go on a journey, and the distance you’ve travelled so far

The triangle, or “delta”, is used to indicate a tiny change in the following variable. Let’s say you go on a journey, and the distance you’ve travelled so far is “x” and the time so far is “t”. Then your average velocity since the beginning is x / t . But, if you want to know your current velocity, that would be delta x divided by delta t . The delta is usually used in a “limiting” sense - you can get a more accurate measurement of your velocity by measuring the change in x during a tiny time interval. The tinier the interval, the more accurate the estimate of current velocity. What I’m talking about here is the first steps in learning differential calculus. You could look for that at kahnacademy.com. You might also benefit by looking at their “precalculus” courses. Just keep plugging away at it, the concepts take awhile to seep in. Attaining mathematical maturity takes years.

simiones 5y ago
I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).
- wrycoder 5y ago
  True. To continue my example, the average velocity in the last hour would be taken with a ∆t of 60 minutes.
- pbhjpbhj 5y ago
  Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t ! Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek. At uni I learnt how to properly write an ampersand (for logic classes) and how to write Aleph and Beth (for pure maths, particularly transcendental numbers). Some professors have a fondness for the more confusing Greek letters (lowercase xi, lowercase eta) ... is it n or eta, epsilon or xi, ...
  - wrycoder 5y ago
    https://en.wikipedia.org/wiki/Riemann_sum https://en.wikipedia.org/wiki/Riemann_sum usually uses ∆. See also the explanation of ∆ at https://en.wikipedia.org/wiki/Derivative#Explanations https://en.wikipedia.org/wiki/Derivative#Explanations . That's the sense in which I'm using ∆, which is common, at least in the US.
    - Jensson 5y ago
      But this is a physics paper, that isn't how you use uppercase delta in physics. It is just a range. In physics however you do a ton of approximations all the time in ways mathematicians hate (you don't care about errors smaller than you can measure), so uppercase delta is often approximated with derivatives etc, but it isn't a derivative. Math in physics is way more practical and uses very different techniques than math in math, often because physicists invented the math first and mathematicians later went and formalized it.

simiones 5y ago

I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).

wrycoder 5y ago
True. To continue my example, the average velocity in the last hour would be taken with a ∆t of 60 minutes.
pbhjpbhj 5y ago
Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t ! Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek. At uni I learnt how to properly write an ampersand (for logic classes) and how to write Aleph and Beth (for pure maths, particularly transcendental numbers). Some professors have a fondness for the more confusing Greek letters (lowercase xi, lowercase eta) ... is it n or eta, epsilon or xi, ...
- wrycoder 5y ago
  https://en.wikipedia.org/wiki/Riemann_sum https://en.wikipedia.org/wiki/Riemann_sum usually uses ∆. See also the explanation of ∆ at https://en.wikipedia.org/wiki/Derivative#Explanations https://en.wikipedia.org/wiki/Derivative#Explanations . That's the sense in which I'm using ∆, which is common, at least in the US.
  - Jensson 5y ago
    But this is a physics paper, that isn't how you use uppercase delta in physics. It is just a range. In physics however you do a ton of approximations all the time in ways mathematicians hate (you don't care about errors smaller than you can measure), so uppercase delta is often approximated with derivatives etc, but it isn't a derivative. Math in physics is way more practical and uses very different techniques than math in math, often because physicists invented the math first and mathematicians later went and formalized it.