I live in Colombia and it's quite common for gangs to charge a "Vacuna" -literally vaccine, but more like protection money. Venezuelan gangs are some of the worse. This is just normal behavior for the part of the world these folks are coming from. This is what happens when you leave your southern border open and don't vet the people coming into your country. Plenty of great Venezuelans in the world, but plenty of horribly violent ones too.
No one has to join the channel if you they don't want to. The goal is to simply provide useful learning videos that hopefully help ... if I'm able to do that, then the video/channel has served its purpose! Happy learning!
Why can you assume that the side pyramids are identical in general to the two original pyramids (from the bottom and from the top)? That is true only when W=H.
Hi! You are correct. This video captures the special case to simplify the understanding of a geometric proof. However, if you would like to see the general case you can. I pinned the general proof video. It is longer however :) … Happy learning and thanks for the comment!
Hi! I am using algebra here to simplify the right hand side by working with the height, width, and depth. I am not sure which term(s) you are referring to, but you can let me know and I will try to follow up. Cheers!
Super happy to see this comment. I don't always know unless people comment and like if the videos are helpful. Glad to see this comment! Super happy to hear the video helped! Cheers! Welcome to 1mjourney!
I am disappointed that you used your result from rectangular pyramid to prove the triangular pyramid. I am expecting that you are going to show “graphically” that a triangular prism consists of 3 triangular pyramids. After some graphical tinkering, I come out with the following: Consider 2 triangles, ABC at the bottom (A,B are front angles, C is back angle) and DEF at the top with corresponding angles. Connect vertical lines AD, BE, CF. Also connect diagonal lines AE, AF, BF. Triangle ABC has depth “d” which is perpendicular to AB. Furthermore, AB=w, AD=h. The first pyramid has base ACB and vertical edge CF. The second pyramid has base FDE and vertical edge DA. The third pyramid requires some visualization as it has a “slanted” apex F. It has base AEB and slanted edge EF, but with vertical height equal to “d”. All the 3 pyramids have equal volume as along as their “wdh” products are the same. For the third pyramid, d becomes the height, and h becomes the depth.
Nice to see your input! Always interested to hear what others think! I put out the video because it was fun to go through just geometry for the proof and do the general case. Happy learning!
In addition to h = H/2, I think you also need W=D=H. You initially mentioned that it is a cube with equal lengths, but your drawings are showing different dimensions. The tips of the 6 pyramids meet at a single point at the center of the cube.
Always fun to see a comment here! The sides are indeed equal of the original cube. Note that the reason why you are seeing the further drawings as of different size as I double up the pyramid to show the result. If you are really keen in understanding the general case of this proof (unfortunately the video for this is much longer) then do not hesitate to take a look: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-F952z0McAhw.html
Great question! the cos 180 has been incorporated, notice that in the video I placed the negative in front of work, or on other words you have 492 * 2.8... * cos 180 = -1380 J. Cheers and hope that helps!
Hi. Notability is the app that I am using for drawing/writing/etc. Unfortunately it is no longer for free. Notability has grown and is now subscription based. I still got it when it was for a few bucks and have all the features grandfathered. Hope that helps! Happy learning.
Good question! There are a few ways to think about this. Here is one way: in this video you saw how to find at least 1 king, so if you want at least 2 kings, then take the complement in this way: i.e. 1 - (no king + 1 king). You can let me know if that helps! Happy learning!
Excellent video, one question. How to reduce the size of photobooth, mine stops going smaller than certain size and that is still to big for my Macbook pro 13" screen. Do you use external monitor connected to Mac ?
Hi! Glad the video has helped. Yes, I do use a monitor. Indeed on the macbook photobooth is a bit bigger, however, you can take it off screen partially and readjusted the camera. I just tried it on my macbook. I noticed that I could adjust it in such a way that it is very close to my monitor view. Cheers!
Typically, the word indeterminate is used solely in the context of limits. A limit of f(x)/g(x) where f(x) and g(x) are both approaching 0 is in an indeterminate form, meaning that some other method beyond direct substitution must be used to find the value of the limit. But as a simple expression, 0/0 is undefined, as it doesn't have a definition. I understand what you mean when you say 0/0 can have "many answers", because any real number could be justified, but no number *is* defined as the value of 0/0, so that expression is undefined. I've never found any textbook or academic resource using the word "indeterminate" to refer to expressions like 0/0 outside the context of an indeterminate form of a limit, and I've looked, because I've found this to be a very common mistake.
Great comment! Thanks for sharing! Indeterminate does not only relate back to limits (in fact this video would not be intended for those studying limits, but studying basic number sets). The question and idea of indeterminate comes up in solving equations. For example if you run into a solution of an equation which yields 0x = 0, in this case it is indeed indeterminate which value of x it would be as any value would work (lets assume its a real number). Now the standard solution of ax=b is x = b/a, but when both a and b are 0, then you get x = 0/0 and hence the indeterminate. Hope that brings some context to the video. Cheers!
@@1mjourney I do see what you mean, that 0x=1 has no solutions, while 0x=0 has infinitely many, but that's not quite the same issue. Division by zero itself is not well-defined, and frequently leads to contradictions, so in solving these equations you wouldn't *literally* divide by 0 and get 1/0 or 0/0. I'd like to ask you to consider the other six indeterminate forms. Five of them involve infinity, and so are nonsensical on their face outside the context of limits. And the last one, 0^0 is in many contexts explicitly defined with a value of 1, and in other contexts, intentionally left undefined. It is just a word, though, and as long as it's clear what is meant by it, it doesn't really matter. But, I do have to disagree that this is a typical way to use "indeterminate". A quick google search of things like "math indeterminate" turns up almost nothing that isn't in regards to limits. All I found were this video, and a Khan Academy video which, although it doesn't mention limits explicitly, says at the end that the term is often used in calculus. And all textbooks, calculators, and CASs that I'm familiar with refer to 0/0 as "undefined".
@@RunstarHomer This is great! I agree with you 100% that indeed there are many contexts where the 0/0, 0^0, limits comes up. It is indeed unfortunate and I will take the fault for not formally defining the exact meaning of indeterminate that I mean in this case. It brings about the importance of clear definitions for the context at hand. I don't have an argument that takes the general case where 0/0 can come up because indeed many contradictions arise. I love when someone comes along and points a hole in one of my videos and reminds me to be careful with the usage of particular terminology. Cheers! And thanks for the comments!
Hi! The set up with the video is ultimately up to you. As you noticed in the video I like that the photobooth nicely allows overlapping which creates a seamless visual recording. I'm sure there are now other visual tools available (especially if you are willing to pay), but the goal was to keep things simple and with free tools. Happy recording!
