It’s really a term from statistics. It’s the same as an exponential growth rate, but you only take the value of the exponential function at discrete intervals.
If you had a function you wanted to graph like 2x, exponential growth is like saying x can be any real number (even a fraction or something) and every part of the line you draw is counted, but geometric growth would be a discrete value for x like [1, 2, 3, …, n] where x is from that interval pattern. It’s useful in statistics for measuring data based on something like time. The examples I was taught were like cells splitting in two at a fixed time interval. You can still draw the graph like it’s a single curve to visualize it, but the actual data points are at discrete values for x and just not in between.
I haven’t had a stats or math class in a long time, but I believe this is correct enough from a quick scan of Wikipedia.
Yeah, that’s basically how I remember it, though it’s not always stats–the terms are used in other fields of math as well. A first calculus class typically includes a proof that the limit of the sum of an infinite geometric series (a + ar + ar^2 + ar^3 + …) tends towards a/(1-r) where a is the first term and r is the ratio of successive terms, provided that -1 < r < 1. (Otherwise the series diverges and the limit isn’t defined.)
Absolutely! I vaguely remember a discussion of geometric growth in at least one other course, but I was doing my best to give a thorough layperson’s explanation without getting into more analytic definitions for geometric series or the concept of continuity. I studied abstract/theoretical mathematics in my undergraduate degree, so I only really remember seeing geometric growth defined in statistics courses as far as applied mathematics goes as I avoided those courses where I could. I’m not in academia, and I did not pursue a further degree, so my apologies if I wasn’t entirely accurate. My mathematical theory is very rusty these days. lol
Oh, I only minored in math, I’m no expert either! Yeah, your explanation was really fine, I just thought the “sum of a geometric series” thing might ring a bell for some readers.
I know a Doctor Pythagoras might have a theory. But it might be irrational to go that route. But you said lumps, so sounds like your developing extra roots. To be absolute, try graphing it. Though it might just get better in a few days, give or take a few.
Anyone care to explain what a geometric rate is?
It’s really a term from statistics. It’s the same as an exponential growth rate, but you only take the value of the exponential function at discrete intervals.
If you had a function you wanted to graph like 2x, exponential growth is like saying x can be any real number (even a fraction or something) and every part of the line you draw is counted, but geometric growth would be a discrete value for
xlike [1, 2, 3, …, n] where x is from that interval pattern. It’s useful in statistics for measuring data based on something like time. The examples I was taught were like cells splitting in two at a fixed time interval. You can still draw the graph like it’s a single curve to visualize it, but the actual data points are at discrete values forxand just not in between.I haven’t had a stats or math class in a long time, but I believe this is correct enough from a quick scan of Wikipedia.
Yeah, that’s basically how I remember it, though it’s not always stats–the terms are used in other fields of math as well. A first calculus class typically includes a proof that the limit of the sum of an infinite geometric series (a + ar + ar^2 + ar^3 + …) tends towards a/(1-r) where a is the first term and r is the ratio of successive terms, provided that -1 < r < 1. (Otherwise the series diverges and the limit isn’t defined.)
Absolutely! I vaguely remember a discussion of geometric growth in at least one other course, but I was doing my best to give a thorough layperson’s explanation without getting into more analytic definitions for geometric series or the concept of continuity. I studied abstract/theoretical mathematics in my undergraduate degree, so I only really remember seeing geometric growth defined in statistics courses as far as applied mathematics goes as I avoided those courses where I could. I’m not in academia, and I did not pursue a further degree, so my apologies if I wasn’t entirely accurate. My mathematical theory is very rusty these days. lol
Oh, I only minored in math, I’m no expert either! Yeah, your explanation was really fine, I just thought the “sum of a geometric series” thing might ring a bell for some readers.
Its the rate at which geometry geometerates geometrically.
I would know, I’m a geometricologist.
I have a lump on my hypotenuse, any recommendations?
I know a Doctor Pythagoras might have a theory. But it might be irrational to go that route. But you said lumps, so sounds like your developing extra roots. To be absolute, try graphing it. Though it might just get better in a few days, give or take a few.
It’s about 1 gigaArnold/s^2
Basically an exponential function.