How to calculate pi-pb roll-over cables


ok the topic today is similarity and relationships and with the topic that we are discussing today, the aspect that connects the subjects, certain mathematical contents become clear again, so to speak, should leave mathematics in part and look at other sciences and yes, the topic of similarities has relationship from different Look at perspectives or perspectives of different sciences


and we actually don't even go into mathematics now, but tie the one you have already been to the Wilhelma in Stuttgart and already some exactly when you go in they come across as the first following animals that are




We will ask ourselves from different perspectives from the point of view of biology, so you will first deal with the world of penguins and then take back another science namely physics to be able to imagine that larger ones also somehow have something to do with physical properties That means we also look into the 40 and at the end look into the math, because the math provides valuable information to answer the question why there are big and small penguins like that



Whole on the world map but the world map then you have to put the emperor penguins down there in the Antarctic or some Antarctic islands so it's extremely cold down here too


The African penguins will live well but the African penguins that I somehow do not know where the only one so far, of course, not particularly well so no what that could be but I always know the African penguins in New Zealand Australia it doesn't fit that he experiences the little penguins in Australia show you Madagascar right away, so exactly South Africa to the south of Africa that it actually also South Africa the country South Africa there live the sun on the beach and imagine that that's true, that's a bit like fish, ok so the African penguins live in Africa what always knew that penguins live in Africa who knows maybe from the movie Madagascar like the Telekom with the 1st train to but the journey to the Antarctic is and escape each other saying exactly whether it is no longer exactly who lives with the African penguins not in a nearby individual who we want to have warm so they live here in South Africa


Example only very precisely


more penguins here were the Galapagos penguins that was also the penguin penguins so you can see a little on the rings around the eyes the ok Galapagos penguin lives well OK on the Galapagos Islands someone knows where they are in Ecuador because of the location at the equator just right so in the Pacific at the equator can imagine that it will get really hot somewhere in Hungary Galapagos penguins live where they were


just as the little penguins you had just mentioned that it is one step smaller it is around 35 to 40 centimeters high so what supports centimeters so good not good children like much bigger both experienced in New Zealand and now that is what I have problems for Linux used at home called it the template for the Linux penguin for Tux is called I think so is the New Zealand Little Penguin should if


Look at it on the world map the penguins experience further processing when he Galapagos penguins become so towards the equator and on the very right the little penguins live so mean and


back the kings against him


By the way, we also live down here in the corner, so point towards Antarctica at hand arctic island what is conspicuous broken about conspicuousness 1.


next hint for us and yes to deal with temperatures with body sizes temperatures and energy and that is immediately in the other science namely in physics not already with the physics glasses on these conditions and can only carry out a small experiment and that has I performed the experiment as follows


they call themselves 2 which glasses are distributed as penguins ok so the lid is also important so that not so much water vapor comes out here and so that energy should disappear from the glass, so to speak, we have 2 beaker glasses that look relatively similar, the 1 only larger than others and now she is because she does not have to fill the water a bit but that makes the feet of the piano and not of a kettle boil relatively quickly as it is best at the same time because the energy is already escaping through the so to speak that becomes Water gets colder because the water is in it then you have your thermometer every year the remaining thermometer is plugged in at the top with which the water temperature is measured that you can see what happens if you let it cool down over a certain period of time what you know alarm clock still


from a time clock and then there becomes


yes every 15 minutes measured here ok so big glass small glass like that and at the beginning I measured 74 degrees Celsius so it wasn't quite 90 100 or so just so cold after the kettle whistled ok so looks in both cases Degree Celsius warm water now I would like your prosthesis What is the temperature profile in the two 1. There are 3 variants Variant a the water cools the two glasses at the same time Variant BB the water cools down faster in the large beaker than in the small and variant C. the water cools down faster in the small beaker than it would in the large one, variant A is not ok 1.


Math to say ok it around an essential




but also to the situation in the


grateful that it still stays on


one can a times B R like a rare always the other change which knowledge I have here K square times


R-square times but mention rearranged and that's just R-square times


A 1 to and the old of the old surfaces in small work such squares but woe if comes to K square miles A 1 so also the security as well as actually exactly K represented he increased the two side lengths K with which one must be modified the computer K square larger becoming ok now we have only looked at rectangular shapes, comma is different from the one we are looking at



ok you can see the personal valet inside times the base side times the height already maybe you can move them can get the two of them then the square times the


Wilex we do all of this, but more of a personal chamberlain cameras through Kagawa, wherever you have or, like at the cash registers, fetched from and then it is just square times A 1 where even with a triangle the area increases by the factor k Crawford area of ​​the circle after such a human posture is the Pi times R-square ok square so what I do now of course now for larger singing circles again evenly so that all lengths are stretched by the factor k so the radius the longer radius becomes by the factor k stretched but never is only short here but 2 = is the same then accordingly the radius it is now K r to the square unfortunately just very much you can pull it ok ne whole K square to the outside stands the K square times Pi R square and that is straight K square


So here, too, the K square size but there is still a fundamental consideration that everyone has with this figure or was it like when I think that these figures factor larger longer factor K what happened of the areas he even welcomes square the trade advised or or reason it was always so is really always exactly so your card has been kept secret so far it is still completely right so also K square get bigger so before exactly K squares but why does my reasoning how could you understand that here justified one the yes every route and but the computer to align difficult not exactly which one there yes exactly 3 we can divide the thing here into triangles so so so so so so and so on and so on and these small 3 lengths with the factor K larger that means the 1st part of these triangles increases the factor K of the square and from a point of view also the whole of the and that is the reasoning say king ok that is completely no matter what a figure looks like, the security is always increased by a factor of k squared by a factor of k stretch, something here yes I can also divide it into triangles is a lot of triangles and there is no such thing as that which is never explained 3 can for those who like these high rates how can I approximate with a low one, the OK square will also be larger as well as the circumference also in summer so conclusion if I enlarge a two-dimensional figure by the factor k with respect to the length of the stop exactly by K square size not by , point 3 K square and not by 7 K square Character therefore needs the area halfway to K square


political the whole thing have already shown briefly is the three-dimensional with three-dimensional interested in particular the volume so we have in cube what happens if I now all excuse nonsense wrong with the small cube, the side lengths are a okay then the volume of course but to the power of 3 what happens to the volume if I add all the side lengths factor K for larger ones


3 he should of course then can only 3 times


1 so I here also here will that means here too the volume is increased by a factor of k to 3 who can go through the same thing that they have done with all possible two-dimensional figures themselves take bodies ball cylinder of the pyramid he will change the volume and end can also be 3 larger if you for example times from the cylinder or from 1 1 o'clock in the cells of exactly that the volume of the unit base side times height whereby the base side for nonsense jokes base side


times the height would be for a cylinder


if you have, for example, the base of its base area by the height, so base by the height, the base is circular shapes and times that if you now know by the factor k stretches who areas grow, factor K square grows in height by the factor k that the whole life would also be again I said and also 3 bigger if you take my pyramids there you have the formula 1 but it works from the 3rd base area times the height that means here too the area will again be larger by a factor of K square belong factor came here again also 3 so no matter which three-dimensional figure you take, the volume will be and weeds 3 will be bigger and now we bring that together


In the ratio of surface area and volume we know if I have the surface O 1 here at 7 o'clock 1 if I multiply in length by k what happens then with O 2 other smooth surfaces are the surfaces are two-dimensional figures, if you like, that's enlarged The volume increases by square after K quadrature if I increase the K segment and can also 3, i.e. if I make something on plus a little larger then the surface grows square and the volume Gubic to the power of 3, which means volume grows much faster than Makes the surface bigger with something that means if something is enlarged or in this form then the volume in relation to its surface becomes larger faster or the other way around the surface 6. less fast and accordingly becomes smaller in relation to the volume and if I now here the volume he forms this ratio of balls O 2 to V 2 1 = is equal to KA quadrature of a purchase price V 1 and the K square for short h against the K when he here simply 1 by K times the old ratio O once by V 1 the old ratio namely surface-volume ratio that got through it I get the new surface and even the ratio is smaller K is larger than it is me So for bigger ones K is bigger than one of the ratio of surface to small the whole


you can also illustrate a bit here with the following picture of the world cubes and ultimately this can also be discussed very well with children at this point they can not only introduce the following we build houses ok houses we are allowed to houses and these little ones are really their little cubes Room that means on the far left is your own house consists of one room, the next house is stretched by the factor k equal to 2, that means here I was 18 at one time and in the big house here I have 3 times 3 times 3 rooms around the Factor 3 stretched from the house so that means I now have different sized houses with rooms and the question is now in winter when it is cold not the houses and the energy goes out over the surface, so over the room walls is always still from the ground, it doesn't matter, yes, in all directions the energy goes out equally of the Kameyama count among the people