Pyramid (exponential) Power (2)

Here is the answer of my math question.

A1.

Assume the 3rd and 4th levels are complete, Hitoshi can get the money: 40^2 * 1000 * 0.25 * 0.9 - 1000 = 359000 Euro. Hitoshi is rich!

A2.

Daniel is the same. Wait, Daniel needs the 6th level of the pyramid. To complete the 6th level, we need:

1+ 40 + 40^2 + 40^3 + 40^4 + 40^5 = 105025641 (around 100 million)> 2.5 million

There is not enough people in Berlin for Daniel. He lost his 1000 Euro every month. and Hitoshi lost Daniel as a friend. ;_; Actually German population is around 80 million, so, even if all the German people joined this, Daniel can not get the expected full payment. Actually next answer shows Daniel has absolutely no chance to get any Euro.

A3.

Hitoshi needs total 5 levels.

1+ 40 + 40^2 + 40^3 + 40^4 = 2625641 > 2.5 million

So Hitoshi's level needs a bit more than the people in Berlin. But if everyone is convinced in Berlin, even babies and children pay 1000 Euro every month, Hitoshi can be rich. (Which is basically impossible.) This also means Daniel has no chance to get any money.

A pyramid system is basically a Monarchy system. The king can get money and it is true someone is the king. So you can see the proof of someone gets the money. But I think the question is ``you'' can be a king or not. Well, good luck for that. I think if Hitoshi saw more than 30 people related with this system, Hitoshi has basically no chance in Berlin, Hitoshi is in the slave level in this case.

Essay question: Why do some pyramid systems try to expand to the foreign countries?

Comments

Why A^{T}A is invertible? (2) Linear Algebra

Why A^{T}A has the inverse Let me explain why A^{T}A has the inverse, if the columns of A are independent. First, if a matrix is n by n, and all the columns are independent, then this is a square full rank matrix. Therefore, there is the inverse. So, the problem is when A is a m by n, rectangle matrix. Strang's explanation is based on null space. Null space and column space are the fundamental of the linear algebra. This explanation is simple and clear. However, when I was a University student, I did not recall the explanation of the null space in my linear algebra class. Maybe I was careless. I regret that... Explanation based on null space This explanation is based on Strang's book. Column space and null space are the main characters. Let's start with this explanation. Assume x where x is in the null space of A . The matrices ( A^{T} A ) and A share the null space as the following: This means, if x is in the null space of A , x is also in the n...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

Why parallelogram area is |ad-bc|?

Here is my question. The area of parallelogram is the difference of these two rectangles (red rectangle - blue rectangle). This is not intuitive for me. If you also think it is not so intuitive, you might interested in my slides. I try to explain this for hight school students. Slides: A bit intuitive (for me) explanation of area of parallelogram (to my site, external link) .

Lx=d: SundayResearch

Search This Blog