Ugh, 3 factorial is most definitely not equal to π. It’s something more like, idk, 9? Honestly I don’t even know how I got here; I majored in Latin and barely past
Seriously, if you’re working with analog electronics, 𝛑=√1̅0̅ is close enough. If you need more precision, use active error correction, and in the 21st century that’s easiest to do digitally anyway.
Imaginary numbers are best understood as symbolizing rotation. If we’re imagining a number line here, “looking back from infinity” - at a scale where Grahams number looks like the mass of an atom expressed in kilograms, i would not be in that infinite set of numbers, it would be a point above that line and creating a perpendicular plane to it.
I hate the term “imaginary” because it’s misleading. Most high school algebra teachers don’t understand what they are either, so people learn about these things called “imaginary” numbers, never learn any applications with them, hopefully graph them at best, and then move on understanding nothing new about math.
Students also tend to get really confused about it as possibly a variable, (it’s really annoying with in second year algebra courses, where e and logs also show up). We say “ah yeah, if you get a negative sign, just pull it out as an i and don’t worry about it. or just say no real solutions.”
I think in precalculus at least, something like this is not too hard to show and explain to a student. This would be a fine “final” thing to end the typical high school math career on - showing how all of the different concepts you’ve explored come together.
Ugh, 3 factorial is most definitely not equal to π. It’s something more like, idk, 9? Honestly I don’t even know how I got here; I majored in Latin and barely past
Barely passed your English classes as well I assume. /s
In case anyone wondering factorial is
n! = n * n-1 * n-2 * … * 3 * 2 * 1
Erm. In what world do you live that the precedent in your expression is right?
In all languages and countries I know multiplication binds more strongly than addition. So what you wrote would be
n^2 - n - 2n - 3n…
I wrote it correctly. It is the definition of a factorial.
No, correctly it would be n * (n-1) * (n-2) * … * 3 * 2* 1
Or the actual recursive definition
1! = 1
n! = (n-1)! * n
What I wrote and the context it makes sense.
E: ohh yeah I see
Yea, reading my message back I was unnecessarily harsh. But my math checks out.
Sorry, I had a bad day…
No worries. It happens
They barely passed me.
Math is a liquid. Or a language.
My high school English teacher still has night terrors about me starting sentences with conjunctions. And that was the least of their problems.
Edit: kind of unrelated, but that song about conjunctions is now stuck in my head. 🎶Conjunction junction, what’s your function? 🎶
π = 1
3! = 10
Seriously, if you’re working with analog electronics, 𝛑=√1̅0̅ is close enough. If you need more precision, use active error correction, and in the 21st century that’s easiest to do digitally anyway.
Well…
g1/2 = e = 3 = pi
3 = 10^(1/2)
e = π = σ = ε = µ = Avogadro’s Number = k = g = G = α = i = j = 3
(at least that’s how they all look when viewed from ∞)
I was not ready for this truth bomb
Shouldn’t have i in there, or j if you’re using that to represent the imaginary number. The complex plane is separate.
Let epsilon be substantially greater than zero…
The list of things I shouldn’t do, but do regardless, stretches past infinity.
Imaginary numbers are best understood as symbolizing rotation. If we’re imagining a number line here, “looking back from infinity” - at a scale where Grahams number looks like the mass of an atom expressed in kilograms, i would not be in that infinite set of numbers, it would be a point above that line and creating a perpendicular plane to it.
I hate the term “imaginary” because it’s misleading. Most high school algebra teachers don’t understand what they are either, so people learn about these things called “imaginary” numbers, never learn any applications with them, hopefully graph them at best, and then move on understanding nothing new about math.
Students also tend to get really confused about it as possibly a variable, (it’s really annoying with in second year algebra courses, where e and logs also show up). We say “ah yeah, if you get a negative sign, just pull it out as an i and don’t worry about it. or just say no real solutions.”
I agree. Although better and more illustrative videos have since been made on YouTube, my favorite introduction to the square root of negative one is Chapter 22 of the Feynman Lectures on Physics Vol. I
Feynman has so much great stuff to plagiarize.
I think in precalculus at least, something like this is not too hard to show and explain to a student. This would be a fine “final” thing to end the typical high school math career on - showing how all of the different concepts you’ve explored come together.