On today’s episode of “you don’t need to spray your entire cologne bottle”, please remember that it is not, in fact, air freshener.
Me not doing an assignment because I don’t care is one thing but you marking an assignment I did as missing, especially when I know I showed it to you, is a whole other
A lot of times I have fallen into this pitfall where I seem to
completely understand how to methodically do something without actually
comprehending what it means.
And only after several years after I first
encountered the notion of cross products did I actually understand what
they really meant. When I did, it was purely ecstatic!
Why on earth is the direction of cross product orthogonal ? Like seriously…
I mean this is one of the burning questions regarding the cross
product and yet for some reason, textbooks don’t get to the bottom of
this. One way to think about this is :
It is modeling a real life scenario!!
The scenario being :
When you try to twist a screw (clockwise screws being the convention)
inside a block in the clockwise direction like so, the nail moves down
and vice versa.
i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move..
That’s why the direction of the cross product is orthogonal. It’s really that simple!
Another perspective
Now that you get a physical feel for the direction of the cross product, there is another way of looking at the direction too:
Displacement is a vector. Velocity is a vector.
Acceleration is a vector. As you might expect, angular displacement,
angular velocity, and angular acceleration are all vectors, too.
But which way do they point ?
Let’s take a rolling tire. The velocity vector of every point in the
tire is pointed in every other direction. BUT every point on a rolling
tire has to have the same angular velocity – Magnitude and Direction.
How can we possibly assign a direction to the angular velocity ?
Well, the only way to ensure that the direction of the angular velocity
is the same for every point is to make the direction of the angular
velocity perpendicular to the plane of the tire.
Problem solved!
I’m still pissed off about that triangle thing though because I labeled the triangle with all the necessary stuff because it said to explain and I had to organize it for myself. But I didn’t label every side and angle, just the ones directly relevant to the problem. But apparently that meant I didn’t understand the problem enough for full credit.
It’s not random, I have modern education as well. I feel for you.
I’ve hated it since it was introduced. It’s horrible.
Common core does suck. It doesn’t teach anything of value.
Like, who does it benefit?
Certainly not the neurodivergent kids.
Common core is based around the idea of making it applicable for everyone, rather than allowing individuals to further themselves in unique ways. To put it another way, it’s like instead of letting a man pick the tools he needs, everyone is given the same 3 tools and expected to get by with just that.
I dislike it because suddenly I went from being in higher math classes with As and Bs to failing because I didn’t show my work, DESPITE all of my answered being correct.
I typically don’t solve math problems in the traditional way and I’d I understand what in doing I will do it all in my head..
This is such an odd concept for me too because every single standardized test I have taken did not require me to show my work for math but for some reason I would have to show my geometry teacher how I multiple the sides of rectangle or get the question wrong.
Honestly I got points off for not showing work in an extreme amount of detail on the test even though I’d labeled the triangle and all that and it was clear I understood the concept and what was going on. Not like it was a problem you could really answer without understanding it anyway.
The only time I can really see making showing work mandatory is if you’re going to give partial credit if someone made a dumb error but still clearly knew what they were doing. For example, mis-writing a number but having the right process.
Outside of that it’s just really stupid because… how am I supposed to know how much work you want me to show? I’m not great at mental math, so I already show a fair amount anyway, but at a point showing work just becomes busy work.
Basically, showing work does have SOME teaching benefits but that’s outweighed by how inconvenient and annoying it is.
wait is 5! = 120 an actual math thing i just reblogged it bc i sincerely believe that yelling a number makes it bigger
An exclamation point after a number means factorial. Five factorial is 5 times 4 times 3 times 2 times 1. Three factorial is 3 times 2 times 1, etc.
But the more exclamation points after a number, the less big it is, a double factorial is every other number, so 6!! is 6 times 4 times 2, which is less than 6!, So yelling a number makes it bigger, but yelling louder makes it smaller again
it’s because you scared it
I genuinely love this post
You know I was going to shut up because it’s the same thing over and over but my math teacher doesn’t seem to understand that this is math class not arts and crafts class.
ifesbob 