Algebra and Mathematics. Explained with easy to understand 3D animations.

Algebra and Mathematics.  Explained with easy to understand 3D animations.


Algebra is the foundation of all science and technology. Algebra is the foundation of economics and engineering. Algebra is a key to understanding logic and everything in the world around us. The goal is to find the number in the red box. The red box is what we call a variable. The red box can appear anywhere in the equation. The question is, what number can we put in the box to make the equation true? All boxes with the same letter on them must have the same number inside. The question is what number we can simultaneously put into both red boxes to make the equation true? In this case, there is only one correct answer. The same number must go into the two blue boxes. A different number can go into the purple box. In this case, there are many correct answers. Life rarely has only one variable. Here, the two blue boxes are one variable. The purple box is a second variable. There are an infinite number of solutions to this problem. Variables can represent positions in space. Here we have three variables. Each can have a different number. One solution is for Y to be 2, and for Z to be 4. This represents moving 2 in the Y direction and moving 4 in the Z direction. Another solution is for Y to be 5 and for Z to be 1. The graph now shows the new solution, and the previous solution. Another solution is for X to be 3, for Y to be 2, and for Z to be 1. The graph now shows all three solutions we have found so far. Suppose we keep adding all the possible solutions to the graph. Eventually, this will be the result. If we include fractions as possible solutions, then the graph will look like this. Every equation has a graph that represents all its possible solutions. If we make a graph of all the possible solutions to this equation, then we will get the following. Now consider this equation. This is one possible solution. And so is this. Since zero multiplied by any number is zero, any values for X and Z are possible solutions, provided that Y is 2. The graph of all the possible solutions looks like this. Now let’s look at all three equations at the same time. What values for X, Y, and Z will make all three equations true? Points that are solutions to all three equations must be on all three graphs. There are only two points that are on all three graphs. Therefore, there are only two solutions. One solution is for X to be 0, for Y to be 2, and for Z to be 4. Another solution is for X to be 1, for Y to be 2, and for Z to be 3. These values will make all three equations true at the same time. We call this solving a system of equations. Here is another way to represent this solution. X weighs the same as one ball, Y weighs the same as two balls, and Z weighs the same as three balls. When the two sides weigh the same, we say that they are equal. This is still true when we replace the numbers with variables. If we make the same change to both sides of an equation, the two sides will still be equal. By making the same change to both sides of an equation, we can find the values of variables. If we add two equations together, the two sides will still be equal. We can use this to find what values will make all the equations true at the same time. We now know that Y is equal to 2. We now know that Z is equal to 3. We previously found that Y is equal to 2. Now we can find out what X is. There is another way to find out what the variables are. Now that there is only one variable, it is easier to find the solution. We now know that B is equal to 4. We can now use the first equation to find A and we can use the third equation to find C. If two variables are equal, one can replace the other. The graph where two variables are equal looks like this. If the equation is modified, the graph changes. To avoid confusing multiplication with variable X, we can use a dot for the multiplication. Or we can write it like this. As the equation is modified, the graph changes. The second green number is where the line intercepts the Y axis. The first green number is the line’s slope. This is always true for all numbers and variables. This is always true for all numbers and variables. C is the distance between the point and the center of the graph. In this case, the distance is seven. This is the equation for all the points with this distance from the center of the graph. The graph of all the solutions to this equation is a sphere. The green number is the radius of the sphere. Multiplying one of the variables squeezes the graph in that dimension. This will be true for all graphs and equations. To understand why this happens, consider a graph with just one dimension. The solutions to the equations are now squished together. Subtracting a number from the variables shifts all graphs. With this equation, each value of Z is a circle with a different radius. This is the same graph and the same equation that we saw earlier. Let’s ignore the X dimension. Subtracting a number from X shifts the graph. This is another way to write the new equation. Now let’s shift the graph in the Y direction. This is another way to write the new equation. These two points will have the following values. These are the solutions to this equation when Y is 0. This is what we call the quadratic equation. We now know how to solve most of the algebra problems we will encounter in life.

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100 Replies to “Algebra and Mathematics. Explained with easy to understand 3D animations.”

  1. This is fucking amazing, I am going to watch all your videos. I have a question, why didn't you use the negative numbers of z on his axis for the graphs?

  2. God bless you for this wonderful video! Every educator ought to show this to anyone willing to watch it.

    I like the music. It makes the video more engaging.

  3. Once again, another one of your videos that made a concept that was once pure gibberish to me understandable. Thank you!

  4. "Algebra is the foundation of all science and technology"??
    C'mon, Eugene, give us a break. All of your graphics are impressive, and almost all your explanations are good.
    With this particular bit of portentous idiocy you make a fool of yourself. Don't do that. You're better than that!
    Algebra is a set of mathematical tools and ideas that are very useful in a great deal of science and technology — but both science and technology go back thousands of years. No part algebra is older than the ancient Greeks, and most of it has been invented in the past few hundred years.

  5. Your Vids are amazing. As an Artist who has had a hard time retaining math concepts you have made it much easier for me. This is excellent! Also, who the artist is that you use paintings?

  6. Jumping straight into 3 dimensions was a bit unorthodox and challenging at first, but is making more sense as I watch more. Thankyou

  7. I'm an ignorant person and understand very little. But I greatly enjoy the music 🎶. As always.

  8. what a brilliant visualizations and explainations sir!!! very very great work sir..i wish your work will reach to each and every one in this world like light!!! thank you very much!!

  9. Isn't z-8 only a shift up when it' s in parenthesis (i.e. (z-8))? And shouldn't x^2+y+2=4 be a cylinder along the positive z axis up to z=4?

  10. i had no idea algebra could account for this much . Once you can describe the shape, form, location, and volume, you pretty much can describe maybe anything. To think some person in the middle east wrote this in the sand playing around with it. I can't imagine the genius. You know, they use to tell us it's just substitution for numbers and values in class. I was robbed.

  11. 1 minute in and this is the craziest video i've seen all year with the weird nature images and Darude-Sandstorm style music

  12. 19:47!!!! That is soooo cool!!!! Also 00:00, 01:26, 07:28, 14:29, 24:46, 27:06 and 37:32(Awesome Pics)……The music is also great…. But the best is from 22:11–24:44, 24:44–25:00 and 32:45–33:56… Great vids…

  13. I wish YouTube should be popular for educational stuff…then life would be so simple for all those students out there…these things are so interesting than game of thrones

  14. This was a great explanation, but the confusion starts at 38:34 where you show other ways of writing the equations. How were those other ways of writing the equations derived?? And the quadratic equations come out of nowhere with no explanation. Maybe it's explained in another video? Also, the techno/trance music is too distracting. Better to use something easy like classical. Thank you for all the content you create! I find it invaluable and have never picked up these concepts so easily.

  15. You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:

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  16. me entering the video: i understand algebra very well there is no way to surprise me now
    me watching the video: … ok i admit i didnt understand the algebra that good before 39 minuits

  17. a video that shows how real mathematicians understand mathematics, visually, they see universes beyond the imagination of all others 👍👍👍👍👍

  18. This is great to visualise abstract ideas.
    I suggest you do math concepts this way for very small children. These will help them think mathematically so at a later stage they will just not become substituion machines. There will be more of Newtons and Einsteins that way

  19. arrrr….too good.
    https://chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

  20. i love your videos, especially the quantum mechanics one, but PLEASE PLEASE PLEASE PLEASE switch off that music. Not only is it highly distracting, but wayyyyy too loud for this. In this video it isnt bearable any more. 🙁

  21. I dont know what to say but this channel is very special
    I hope one day when I will earn i will definately help this channel

  22. All those who hate Math need to see this! They'll love it in no time! Kudos to you Eugene! Your hard work is very much appreciated. Keep it up.

  23. Plzz plzz upload more more more on maths because this types of videos gives different view to understand

  24. To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).

    –To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable.

    –To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video.

    –If you believe that the translation in the subtitles can be improved, please send me an email.

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