Swap the numbers

Hi,
I am reading a book from Matt Parker now. It is called “Things to make and do in the fourth dimension” and the ~200 pages that I read are quiet amazing. The author is also YouTuber and it seems that he mostly does “Standupmaths” which is cool channel. I got inspired a bit and created this game that I started to call “Swap the numbers”.


I was thinking about battery on my phone and how it is going down and that it would be interesting, if the first and second number swapped with the first after subtraction of 1,2 or 3 or more percent at a time. I wrote down bunch sequences, beginning with 100 and going down by one digit numbers.

It is not finished since I want to find a way to predict how these sequences form and I have not figured it out yet. I will give an example and then show why this game is so peculiar.

Let’s say that we subtract the number four, that is the one that I started with:

100 (subtract four) 96 (swap both digits) 69 (subtract four) 65 (and so on…) 56 52 25 21 12 8 80 76 67 63 36 32 23 19 91 87 78 74 47 43 34 30 3 -1 10 6 60 56 65 61 16 12 21 17 71 67 76 72 27 23 32 28 82 78 87 83 38 34 43 39 93 89 98 94 49 45 54 50 5 1 10 6 60 56

If you quickly go through these numbers you will find out that they repeat. When the “10” appears for the second time it starts to repeat. (I also forgot to say that if there is negative number it will act as positive on the “swap” step.) For some reason, many of these “constants” that I start with, end in lapses of “tens” meaning that after “-1” there is “10” and then that is the cycle until new “10” appears. First few numbers have the length of the cycle or lapse “36” or “12” and so far, there seems to be only “1 and 10” as constants that will pull it down to zero. (Also 100 but that is trivial and I have not checked some that could be obvious.)

I have made a program in Delphi 7 to write for me all the numbers for any given constant, that is useful but I will still have to consider the mechanism itself to start to understand it.

Dragallur

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I have 420 likes on FB and it is completely useless

Hi,
so today I reached 420 likes on my Facebook page. Page that connects directly to this blog. That is almost two times as many followers on the blog itself, after more than two years that is certainly not much but I am surprised how I got those likes on Facebook and how pointless they are anyway.

420

It says that I will soon reach 500 and that I should give them money so that I reach it sooner.


Since I do not post very often here, I am not preparing the posts very long time (like today), I do not get many more followers on WordPress. Most of the views come from some searches on Google and somehow people tend to be very interested in this post because it has about 7 or 8 times as much views as any other one, exactly 1,066 as of 17.7.2017. I guess most schools in USA learn about HClO4 and HClO in winter and that is why I have most views in that time of year even though it was such a long time since I wrote the post.
So, I have got 420 likes and it is completely useless. Why? Because when I share something on the page most people do not even see it on their “walls” (yes, I have an option to “market” my post for money so that more people see it which is completely absurd). Anyway 420 is a number that has something to do with cannabis and it is 42 times 10 which is nice.
420 is these numbers multiplied together: 2;2;3;5;7. Those can be accidentally also written like this:
a_0=2
a_n=a_(n-1)+ceil((ceil(√(n-1.5))^2)/3)
That took me at least half an hour to come up with. The function “ceil” takes the number and rounds it up. I hope it creates the numbers correctly. Well that reminds me that you can create a game from this. I am going to do that in school. Just pick few numbers and then try to write either sequence or equation that fits it. That is actually quite endless game with lot of possibilities and variations. Maybe one could say that they will use only exponents for example though I think that it is much easier with all those other fancy functions that make the numbers “nice” like rounding up.
Well I might try another number another day.
Dragallur

Why are cells so small?

Hi,
ever wondered why you have to use microscope to see cell? Well cells are small but why?

There is a simple geometrical reason for it and it has to do with volume and surface area. First let’s take the case of cell being very big and what it would mean for it.

Such a cell would have much greater volume because of greater diameter, that is quite logical, but if you compare it to the surface area (which also increased) the ratio between the two attributes increased, meaning surface area did not grow so much as volume.

Volume (no matter the shape) grows rapidly with the function d^3 where d is the diameter [1]. On the other hand, the surface area only with d^2. So, what this means for the cell is that the surface = the membranes, are going to need to work extra hard to feed and clean up the rest of the big cell. This has some limit and that is why cells tend to be rather small and only viewable with microscope.

If the diameter is 1 than both volume and area are 1. (ratio 1/1=1)
If the diameter is 3 than volume is 27 and area 9. (ratio 27/9=3)
If the diameter is 5 than volume is 125 and area 25 (ratio 125/5=5)

The cell also cannot be too small otherwise the “equipment” (organelles) would not fit in.

Dragallur

Source: https://www.youtube.com/watch?v=wuXSEOKNxN8

[1] Take a cube for example the equation for its volume is V=a^3 where a is the side.

What if the school was a RPG?

Hi,
imagine if one day you came into school and there would be 5 groups in the class. Each one of them had their own character sheet with an information about the character which they are in control of. You would pick the name, place in the world and what does he or she does. Some information might be chosen by the teacher if it would be needed, like the time in which the person lives.


I am thinking up some random rules that I thought would be interesting.

For example, the character would have certain amount of energy and it would sleep well only if you would solve some math problems. Teacher has in curriculum to talk about how the people lived? No problem, it is winter and they need to get clothes (maybe the sellers speak in English) but the groups do not have enough money so they can either teach the seller how to write (because for some reason that is exactly what he needs) or they must find how to get money, maybe by painting pictures about what happened so far or helping design a bow or even build a prototype. Because everybody needs to eat, they will go to forest and learn about plants that are useful for eating and maybe even cook a food and decide if the character liked it or not. On the road, they meet a traveler and they need a water from him because it is a dry season, he has it but needs information about the situation in kingdom. Because they are so far away they need to write a letter to their parents about what happened, of course it needs to be grammatically correct. Finally, after completing their quest they can use the time machine and move into different era, maybe they want to meet with people from their parent’s generation or see a tyrannosaurus rex.

My point is, I personally would be so much engaged in something like that! I am not necessarily proposing it as a true model for schools but I find it to be creative solution to many problems in school though some might still stay, what if a kid is not happy with the character or with the style of RPG? (Well not that many kids like the system these days.)

The thing is that it is an adventure, not just sitting in a school and writing down notes, you are living what you are learning and I would learn german if it was either my character lives or my character dies.

Dragallur