8. The largest building by

8. The largest building by https://padlet.com/hubertproal/2zfp54dbkemsovbx Threads of discussion between MaSuD 2022-2023 students of topic n°8 en-us 2022-11-02 14:50:10 UTC 2026-01-20 10:20:22 UTC hello@padlet.com Please introduce yourselves. Name, age,institution... hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2366820316 2022-11-02 14:51:34 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2366820316 Write down the ideas and progress of yourgroup on your topic hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2366821314 2022-11-02 14:52:05 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2366821314 Hello! My name is Ioana Gavrila, I am 17 years old and I am from "Emil Racovita" National College. I like reading SF books and I am passionate about science since I was a little kid. That's why I am really excited to be part of this reserch project. Also, I like to meet interesting people and to make new friends, so I hope that we will meet this year and become friends! gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369731646 2022-11-04 07:41:57 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369731646 Hey! My name is Sofia Bud, I am 17 years old and I am from "Emil Racovita" National College, Cluj-Napoca. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369732294 2022-11-04 07:42:38 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369732294 We start to analyse some cases for obtaining a formula. We try to find a demonstration for the formula and a posibility for build a 10 m construction gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369736266 Ioana Gavrila]]> 2022-11-04 07:46:57 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2369736266 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2376706900 Hello, I am Ana Selejan, 16 years old. I’m from “Emil Racovita” National College]]> 2022-11-09 12:29:30 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2376706900 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378793603 Hello! My name is Amélie Cannet, I’m 15 years old and I’m from « Val de Durance » at Pertuis, in France.

]]> 2022-11-10 15:12:01 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378793603 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378793757 Hello! My name is Lisa Coraboeuf I’m 15 years old and I’m from « Val de Durance » in France ]]> 2022-11-10 15:12:03 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378793757 We found a formula to refute the fact of making a regular construction : n/n+1. If we choose to say that one kapla= 1, the construction will not be longer than 1. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378798198 Amélie Cannet]]> 2022-11-10 15:14:39 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2378798198 For the first question, we think that we can build a 10m building only theoretically, because in reality, when we have external factors like wind or precipitations, the building will not resist. To calculate the number of pieces that we need for the building, we discover that there are two possibilities to make a 10m construction: the first mode is the classic one and the second one is putting the pieces in a "V" form by following the rule. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2381642372 Ioana Gavrila, Colegiul National "Emil Racovita"]]> 2022-11-13 16:09:06 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2381642372 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382531214 Hello ! I’m Lana Devals, I’m 15. I’m from « Val de Durance » high school in Pertuis,France. ]]> 2022-11-14 08:45:50 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382531214 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382806733 Hello! I'm Adrien Siquot, I'm 15 years old.
I'm from " Val de Durance " in France]]> 2022-11-14 12:41:59 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382806733 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382810444 hello! I'm Andrea Perrot, I'm 15 years old.
I'm from "Val de Durance" in France]]> 2022-11-14 12:44:53 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382810444 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382814204 Hello !
My name is Dorine. I'm 15 years old.
I am from Val de Durance in Pertuis in France.]]> 2022-11-14 12:47:49 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382814204 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382817785 Hi, I'm a student from "Val de durance", Pertuis's Highschool, in France. I'm Titouan Marchais and I'm 15 years old.]]> 2022-11-14 12:50:32 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382817785 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382824767 Hello!
I'm Hugo and i'm 15 years old.
I'm from Val de Durance in Pertuis in France ]]> 2022-11-14 12:55:42 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382824767 hello https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382827641 I'm Antonin and i'm 15 years old .
I'm from val de durance in Pertuis in france ]]> 2022-11-14 12:57:55 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382827641 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382832704 If we cut the kapla (1) in 5, we can see that if we do a regular construction it works with 5 kaplas.

]]> 2022-11-14 13:01:35 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382832704 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382834815 But with 6 kaplas, it fall.]]> 2022-11-14 13:03:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2382834815 Hello, my name is Mateș Ilinca, I am 16 years old. I am from "Emil Racoviță" National College, Cluj-Napoca. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386490969 2022-11-16 12:22:57 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386490969 Greetings 🤗 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386506445 I am Florin Lazăr and I study at “Emil Racoviță” National College in Cluj-Napoca. I am 16 years old, I like to listen to music and to explore new things and my favorite part of day is night, when i sleep. I am thrilled to be part of this project and hope that in the end we will have been on an amazing journey together. Thank you]]> 2022-11-16 12:35:31 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386506445 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386522277 let’s take 3 bricks for example. we observe that in order to achieve the most amount of overhang, we need the 2 areas (red and green) to be equal (assuming that the densities in the bricks are homogeneous), so that the center of mass of the two bricks on top is directly above the point A ]]> 2022-11-16 12:49:02 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2386522277 Hi! My name is Iosif Stefania and I am 16 years old. I am from "Emil Racovita" National College, Cluj-Napoca, and I'm a student in 10th grade. I really like chemistry and biology, but I also enjoy painting and cooking. I am a really sociable person and I look forward to collaborate with you on project. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387225089 2022-11-16 19:50:03 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387225089 We are trying to decide between 2 ideas on how to solve this problem. This is the first one, but as we wrote there, it only work theoretically. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387233233 2022-11-16 19:56:14 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387233233 This is the second one. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387233917 2022-11-16 19:56:48 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387233917 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387926250 Hello ! My name is William, I'm 15 years old and I'm from "Val de Durance" at pertuis, in France. My favourite subject in school is Chemistry. I really like to eat, watch Anime and sleep:)

]]> 2022-11-17 08:40:28 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387926250 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387927047 Hi!!! My name is Marion Court, I am 15 years old and I am from "Val de Durance" at Pertuis, in France.]]> 2022-11-17 08:41:19 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387927047 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942009 Hello!
My name is Léonie. I'm 15 years old.
I'm from Val de Durance in Pertuis.]]> 2022-11-17 08:55:13 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942009 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942087 Hello!
I'm Louise and I'm 15 years old. I'm from Val de Durance in Pertuis.]]> 2022-11-17 08:55:18 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942087 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942383 Hello ! My name is Tom Raffin I'm 15. I'm from Val De Durance high school, in France.]]> 2022-11-17 08:55:35 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2387942383 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388110629 Hello, my name is Nathan Thélu, I'm 17 years old and I'm from "Val de Durance", Pertuis, France. I like maths, music and video games and I can't wait to work with you !]]> 2022-11-17 11:22:56 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388110629 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388112304 Hello my name is Evan. I'm 17 years old.I'm from Val de Durance in Pertuis. I LOVE MATHS and sport. i have language difficulties in English.]]> 2022-11-17 11:24:19 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388112304 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388113795 Hi! My name is ROBERT-VIGANI Sacha and I am 17y.o, I work at the "Val De Durance" school at Pertuis and I can't wait to work with you all. I hope we will be friends and that we can solve this problem !]]> 2022-11-17 11:25:32 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388113795 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388113810 Hey, my name Edouard Siegel. I'm actually 17 years old. I live in Pertuis and I study in the "Val de Durance" high school.
I will enjoy work with you in the next week!]]> 2022-11-17 11:25:33 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388113810 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388114131 Hello, my name is George and I'm 17 years old. I'm from Lycée Val de Durance and I love mathematics. I'm glad to be part of this project and I hope that we will meet this year!]]> 2022-11-17 11:25:41 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388114131 With this one we found that it's possible to do it with e^20 blocks and we're working on the demonstration https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388115894 Thélu Nathan]]> 2022-11-17 11:27:22 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2388115894 in a case where the number of kapla of over lead is odd then the center of gravity is in the middle of the central kapla. if the number of kapla of over lead is even then the center of gravity is in the median of the middles of the central kapla. so that the over lead does not fall and is regular then it is necessary that the result of y-1 divided by y is lower than 1 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2392542620 2022-11-21 12:43:53 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2392542620 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2392549848 Today we try irregular construction. We found some results.]]> 2022-11-21 12:50:06 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2392549848 Hello, I'm Mélisse and I'm 15 years old. I'm from Val de Durance in Pertuis. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396582484 2022-11-24 08:49:44 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396582484 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396588738 The spacing is equal to 1/N so when N increases x also so the variation N is canceled because x varies exactly at the same time.

x= the spacing
N= number of kapla

x+( (N-2)x+1)/2=1
2x+Nx-2x=2
2x-2x+Nx+1=2
Nx=1
x=1/N

]]> 2022-11-24 08:56:26 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396588738 Today we found that if we can prove that a suite inferior to the suite (1/2+1/4+1/6+1/8+...+1/2(n-1)) have a limit that goes toward the infinit, then our suite goes toward the infinite too. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396754613 Nathan Thélu]]> 2022-11-24 11:28:42 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2396754613 In order to achieve the required length of 10 meters, using bricks of 60 cm each, we are going to end up with an equation like ( sum(k=1, n-1) of (1/2k) )*0.6 + 0.6 = 10, where n is the (smallest) amount of bricks we need to use. thus sum(k=1, n-1) of (1/2k) = 15,(6). we can notice the fact that there's a big chance that the sum won't be exactly equal to that value. we therefore are searching for the smallest value of n such that sum(k=1, n-1) of (1/2k) > 15,(6) (by 15.(6) we understand 15.66666... ). after some intriguing research i found out that, firstly, it's hard to calculate n and, secondly, that n is somewhere between 6000022499694 and 44334502845081, which is not a great place to be in, really. would you guys suggest we make a code that can calculate a better value of n for us? the big issue i think we could face on something like that is the fact that the code should be able to work with a lot of decimals, which i personally don’t know how to implement. thank you for reading. let me hear your thoughts. <3 lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398732784 Lazăr Florin]]> 2022-11-26 19:46:06 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398732784 It's true that using your second method, the number of blocks will be minimum, but the classical rule will not be totally respected. I mean that initially, the series for that sum will be 2(1+1/2+1/3+..+1/n/2), and in this case to calculate the length we only calculate 1000/60 because the length will grow with 30 cm per block. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398734900 Ioana Gavrila, Colegiul National "Emil Racovita" ]]> 2022-11-26 19:53:11 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398734900 that value n i talked about earlier is going to be useful in calculating the hight of the construction (0.1 * n meters) lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398735348 Lazăr Florin]]> 2022-11-26 19:54:57 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398735348 Also, we realize that we can't do a c++ program for the classical rule to calculate the number of blocks for any length because at some point there will be too many decimals and the variables which can be double or float can't retain. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398736740 Ioana Gavrila]]> 2022-11-26 19:59:40 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398736740 as nathan mentioned earlier, any amount of overhang is theoretically possible, but only theoretically. things that inhibit us from achieving huge overhang lengths like 100 meters include basic physic realities such as wind, the fact that substances are not atomically homogenous or even gravitational realities, that tell us about how gravity is formed and the fact that as we move further away from the earth, the force of gravity experienced decreases. on second thought, the last consideration could give birth to an entirely new way of viewing the problem. unless i'm going to have a stroke figuring/overthinking this stuff out, i'm going to share my future conclusions with you asap. xoxo lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398740180 Lazăr Florin]]> 2022-11-26 20:09:05 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398740180 something realistic i suggest we all work on is proving why we use the sum that we use ( sum(k=1, n) of (1/2k) or in other symbols: 1/2+1/4+1/6+... and so on ). i made a post a few weeks ago saying: "let’s take 3 bricks for example. we observe that in order to achieve the most amount of overhang, we need the 2 areas (red and green) to be equal (assuming that the densities in the bricks are homogeneous), so that the center of mass of the two bricks on top is directly above the point A". I included the attachment from that post here as well. I believe that using a similar thought process and then some induction theorem thing is going to get us the proof we need. I would gladly do this right now, though i have to go to bed. can't wait to see the progress y'all made 2morrow! lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398746065 Lazăr Florin]]> 2022-11-26 20:28:05 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2398746065 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2400149558 Today we try to do the biggest irregular construction. At the beggining, the distance between 2 kaplas is 4,75cm and at the end the distance is 0,15.

Amélie Cannet]]> 2022-11-28 13:02:08 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2400149558 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2400446806 beautiful ]]> 2022-11-28 15:50:04 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2400446806 We tried irregulars markets. We had thé idea to divide the distance of the spacing by 2 each time we add a kapla. We found thé formule winch allows us calculate thé spacing x in relation to the number of kapla. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2413987659 2022-12-08 07:27:21 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2413987659 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2414197874 when ln n tends to + infinity, ln n = (1+1/2+1/3+1/4...) so :
2 ln n = 10
ln n = 20
n = e^20 = 485165196 kapla
But we have to prove that when ln n tends to + infinity, ln n = (1+1/2+1/3+1/4...) because it is not a reliable source.]]> 2022-12-08 11:30:13 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2414197874 Hello https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2414399662 I'm Claire and I'm 15 years old. I'm studying in Val de Durance.]]> 2022-12-08 14:33:39 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2414399662 umm... no https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2415361592 2022-12-09 08:30:14 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2415361592 Irregulars markets louisebarouch https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416703795 Today we implemented the formula 1/2 exponent n-1 and found that it was not possible to exceed 1.]]> 2022-12-11 09:47:09 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416703795 guys the formula is 1/2 +1/4 +1/6 + 1/8 + ... and so on, which does not have a real limit, being able to be equal to any real value, thus proving that any height can be theoretically proven. the only issue is we need to prove that it is, in fact, the correct sum, which it is lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416881382 Lazăr Florin]]> 2022-12-11 16:18:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416881382 what I suggest we do is that we try to use induction theorem. is it true for one brick? yes, because the center of gravity of the brick above the base-brick will fall right on the edge, meaning that if it were any further away, it would fall. which is important, because we are looking for the max amount of overhang lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416884292 Lazăr Florin]]> 2022-12-11 16:23:57 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416884292 for a building made of three bricks, we are going to use the previous construction and put it on top of another brick, with a 1/4-brick-lenght extra overhang. what do we achieve? exactly, the max amount of overhang possible, because G falls right on the edge. which is precisely what we wanted. lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416890642 Lazăr Florin]]> 2022-12-11 16:35:48 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416890642 we have proof for max amount of overhang for 2 bricks = S(1) = 1/2 and max amount of overhang for 3 bricks = S(2) = 1/2 +1/4. we need to prove the general formula of S(n)= 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + ... +1/(2*n). Come on team, let's do this #teamworkmakesthedreamwork lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416893385 Lazăr Florin]]> 2022-12-11 16:40:39 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2416893385 It is true what Florin said, but for using induction we need to intuit a general formula. We searched on Internet, but all that we found was a calculator for that sum, but with no explication for a formula.What I suggest is to try to answer the other two questions and maybe we will find some formula to use for that sum. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417807290 Ioana Gavrilă]]> 2022-12-12 14:03:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417807290 For example, for the last question, we could easily prove that it is impossible for some shapes, like pyramid, to build a construction following thar rule. But we can study if we can do a building using cubes. I think that it would be interesting to use some lego for this and to see what happens. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417818362 Ioana Gavrilă]]> 2022-12-12 14:10:08 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417818362 Also, for that sum, after doing a short research on Google, I found out that our sum is called a "harmonic series" and it's a divergent series. This was proven by Nicole Oresme in the 14th century. So, it seems that it is not really possible to find a general formula for that sum. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417833693 Ioana Gavrilă]]> 2022-12-12 14:20:01 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2417833693 Dear Ioana, firstly, thank you for your feedback, it really does mean a lot. secondly, although I agree with most of what you say, i don't think that using Legos for this specific occasion would be appropriate, considering the fact that we are looking to build the building so that the bricks themselves don't experience friction with one another. In other words, I believe that using the "kapla" method our french collègues have come up with is the right way to approach this problem. lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2418249732 Lazăr Florin]]> 2022-12-12 18:56:56 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2418249732 in order to apply induction we need to think of the building process as being from below. each new piece needs to be added at the bottom, so that the upper part will be conserved. what we need to find out/prove is the max value of the ratio between the newly provided overhang and the length of the standard brick. research shows that is has to equal 1/(2*n). if we succeed in proving this, then we are going to be able to obtain the desired sum and go to bed feeling just a little bit better about our lives. lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2418267101 Lazăr Florin]]> 2022-12-12 19:10:11 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2418267101 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2420488745 we tried to do the induction based on surfaces
Sofia Bud]]> 2022-12-14 12:43:37 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2420488745 Florin, I agree with you and I think that it is a good idea to use that kapla game that our french colleagues suggest using. Also, as Sofia said, we tried to start the induction part, but we have a problem here because we don't know how to finish the demonstration. If you find a more easy method to solve it, please tell us. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421153975 Ioana Gavrilă

]]> 2022-12-14 22:30:47 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421153975 For being more specific, we tried to demonstrate that the sum we need to find is 1/2+1/4/..+1/2n and for this we used induction. For the first part, named the verification part, we just checked if our statement is true for the minimum number of pieces(2) and for the second part, we assume that the formula is true for k pieces and tried to demonstrate that it is also true for k+1 pieces. What we already know is that the surfaces A and B marked on the photo that Sofia sent has to be equal. We tried to calculate the new surfaces after adding one piece(that k+1 piece) but we couldn't finish. After we will succeed to demonstrate the formula, we will try to find a way to simulate the building process using some online programs because we think that it will be an amazing way to see how things works. Also, even if we can't do a C++ program to calculate the length of a building of x blocks, we thought about finding an alternative or doing this only for small numbers, just to see how it works. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421161737 Ioana Gavrilă ]]> 2022-12-14 22:47:07 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421161737 What do you think about having all access to a document where we can put our main ideas for this research? I ask this because I think that there are many parts that we will forget to use, cause are too many messages here.P.S.: Don't get me wrong, I'm truly happy that we communicate so much, but I think that is a better way for us to keep the information condensed. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421165881 Ioana Gavrilă ]]> 2022-12-14 22:56:08 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421165881 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421585578 how would you translate "induction" please (i don't know what it mean )]]> 2022-12-15 08:55:48 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2421585578 As Wikipedia would say, 'Mathematical induction is a method for proving that a statement P(n) is true for every natural number n'. There are 2 cases that you need to study: the base case is the first one when you prove that p(minimum number) is true. The second step is the induction part, where you demonstrate that if p(k) is true, p(k+1) is also true. I think that for a better understanding, you should read about it on the Internet. gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2422239527 Ioana Gavrila]]> 2022-12-15 18:57:02 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2422239527 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2424693213 facts]]> 2022-12-19 11:22:15 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2424693213 Hey guys! We made some progress on the problem and included it all in a document. We included lots of pretty pictures and words as well. It's not the end result, but we sure are proud of it. Would you be interested in seeing it? let. me. know. lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430620654 Lazăr Florin]]> 2022-12-30 09:45:23 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430620654 Hey ! My name is Laura, I'm 17 years old and studying in Bellevue high school in Alès. It's my third year of Masud and I'm always enjoying working with you. https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430811363 2022-12-31 00:40:53 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430811363 LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430812442 Hey ! I'm Laura and I wasn’t active these days but I read all of what you said and you have such great ideas !
First of all, I made a python program of each proposed construction to check if the constructions don’t fall, if they can be optimised (with the limit axis) and to calculate the total length. ]]> 2022-12-31 00:48:50 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430812442 LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430812596 2022-12-31 00:50:04 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430812596 LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430813108 For now the largest construction is the last one so here is the program if you guys want to manipulate it by changing the number of bricks or anything else : https://drive.google.com/file/d/158ZY7-4AIXmXfeD9fY4vszf3ee1aOay7/view?usp=share_link]]> 2022-12-31 00:54:13 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430813108 LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430814489 Then doing that I realized that the surface of each side of the limit axis is not enough to prove that the construction doesn't fall because with this hypothesis bricks can be anywhere (I tried it with the program and it doesn't work). We have to prove it by calculating the moment of force of each side which is a physic formula, here is a video to understand that : https://www.youtube.com/watch?v=22VGQM1jCn8]]> 2022-12-31 01:05:03 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430814489 LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430815239 We have now algorithmic proofs and modeling but mathematical demonstrations are missing. Tell me what you think or if you have any questions...
By the way, that's great what you did Florin, it will be with pleasure to see your document :)
Laura]]> 2022-12-31 01:10:30 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430815239 Hi, Laura! I think the python program is great because it brings us the possibility to see how the tower is built. We also used physics to deduce our formulas, but we used a lot of the properties of the center of gravity. Moreover, I have a question for all of you because I am a little bit confused: What do you understand from the last question ( the one with the different shapes)? Do you understand that we should study the problem for different dimensions or for shapes like a cub, pyramid trunk, etc? gavrilaioanavaleria https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430900790 Ioana Gavrila]]> 2022-12-31 11:04:11 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2430900790 Hi Ioana, for the problem about the differents dimensions and shapes, I think we should first focus on the main topic of the subject. Then when we think that we have a good solution about it, we'll be able to find better answer for the differents shapes https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2434564309 Nathan Thélu]]> 2023-01-05 11:59:04 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2434564309 Hi ! My name is Bilel, I'm 17 years old and I'm a student from Val de Durance in Pertuis. I like maths and I do a lot of basketball and I can't wait to work with you ! https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2434567451 2023-01-05 12:04:33 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2434567451 You are right Nathan even if we can start to think about it. For example, cubes can be okay because they have also the form of parallelepiped as a brick. But for pyramids and trunks I don't know how we can pile them up without them falling. LauraSum https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2437625914 Laura Sumarriva]]> 2023-01-09 11:36:43 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2437625914 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2437713229 We found this formula to know how to arrange the blocks.]]> 2023-01-09 13:02:18 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2437713229 Hello! https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2440744942 My name is Alexia Puiac. I am 17 years old. I am from Colegiul National “Emil Racovita”. ]]> 2023-01-11 12:35:52 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2440744942 we tried another idea https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2448253748 our teacher said that the construction doesn't have to look like in the picture, so we decided to go with this idea: we only need 153 bricks, and we can also optimize it.
Iosif Stefania]]> 2023-01-18 12:28:09 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2448253748 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2448256254 We thought about leaving space between the brick in order to optimise the construction. We could leave more space, but we haven’t discovered a rule yet.

Mateș Ilinca

]]> 2023-01-18 12:30:42 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2448256254 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2457471116 Would you know how to find the limit of a sum ?

Evan Magnier]]> 2023-01-26 11:37:05 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2457471116 the sum we end up with is actually equal to half of the harmonic series, which approaches infinity, which means that our sum also does that. this basically means that any amount of overhang is possible lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2458227841 Lazăr Florin]]> 2023-01-26 21:22:44 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2458227841 Hi! My name is Ioana Birou. I'm 17 years old and I'm from Colegiul National "Emil Racovita". https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2459746778 2023-01-28 11:44:51 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2459746778 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2461329640 We started to find a formula for this construction.
Amélie Cannet]]> 2023-01-30 12:59:19 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2461329640 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2461701178 Hello! My name is Cristina Lazar. I’m from ‘Emil Racovita’ National College in Cluj Napoca. I’m 17 years old, I like to read and I also play the guitar in my free time :) ]]> 2023-01-30 16:31:18 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2461701178 10/01/2023 hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2462058913 Presentation to the Val de Durance High School researcher.
Yves PAPEGAY - INRIA Sophia Antipolis]]> 2023-01-30 20:24:49 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2462058913 We found a physic simulator in order to simulate the kaplas. Here it is : https://app.physion.net/ https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2500985278 Robert-Vigani Sacha]]> 2023-03-02 11:52:31 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2500985278 Documents for the common presentation at the Nice Congress hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529400404 2023-03-23 19:45:48 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529400404 Logo MaSuD hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529400807 2023-03-23 19:46:11 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529400807 Logo MeJ hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529401106 2023-03-23 19:46:31 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529401106 Logo ERASMUS hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529401384 2023-03-23 19:46:52 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529401384 20/03/2023 hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529404040 Presentations at Marcel Pagnol College]]> 2023-03-23 19:49:30 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529404040 21/03/2023 hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529405198 Presentations at Marie Mauron College]]> 2023-03-23 19:50:44 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529405198 8/2/2023 hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529415452 2023-03-23 20:01:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2529415452 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2540551364 2023-04-01 09:23:13 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2540551364 https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2541298346 2023-04-02 19:05:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2541298346 comment ca va, mes amis? lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2567024999 2023-04-25 10:14:27 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2567024999 do any of u have experience with latex? lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2570606120 2023-04-27 15:56:30 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2570606120 hello lovely people! how are you? how has life been? i hope all of you are doing well. i understand if you might not be in the mood for math, in this moment in time, i surely am not, but we do need to finish this project we have been working on these last months. from what my teacher told us, we need to make a final latex document, a sort of research paper, containing everything that we did. i actually started one and me and my team are currently working on it, but we can only do the method that we worked on (the harmonic stacking). this is why i strongly encourage you to also start writing your parts and submit the "latex code" in the chat in time, so that i can include them in the final document. i'm suggesting this in the hopes that you agree, but if any of you don't and would like to be in charge of putting all of our parts together, please let me know. from what i know, there can only be a maximum amount of 3 collaborators on the free version of overleaf (the latex program), so i won't be able to share with you the document before it's finished. but, when the time will come, and the document will be finished, i will be able to convert it to a pdf document, which is much more easily shareable, and send it to you. our deadline is somewhere in june, i believe, so please treat this final task with the diligence that it deserves. lazaralexandruflorin https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2580944914 miss you dearly, florin]]> 2023-05-07 16:43:50 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2580944914 06/04/2023 hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2584806656 Presentation at the MATh.en.JEANS congress at the University of Nice]]> 2023-05-10 03:35:22 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2584806656 CNER (Cluj) group 1 arianavacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639449745 2023-07-06 06:59:51 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639449745 CNER (Cluj) group 2 arianavacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639450970 2023-07-06 07:01:56 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639450970 CNER (Cluj) group 3 arianavacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639451275 2023-07-06 07:02:26 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639451275 Research poster (CNER) arianavacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639452409 2023-07-06 07:04:14 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639452409 Interactive presentation @MATh.en.JEANS Congress - 7 April 2023 arianavacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639490580 2023-07-06 07:56:20 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639490580 Nice Congress hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639513188 Slide show of the presentation at the Nice congress]]> 2023-07-06 08:28:12 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639513188 Poster presenting a group from Pertuis hubertproal https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639514099 2023-07-06 08:29:48 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2639514099 Poster Satu-Mare proalh https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2649790304 2023-07-23 18:59:50 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2649790304 The research article ariana_vacaretu https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2653993418 2023-08-01 06:01:29 UTC https://padlet.com/hubertproal/2zfp54dbkemsovbx/wish/2653993418