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Write down the ideas and progress of yourgroup on your topic

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Write down the ideas and progress of yourgroup on your topic

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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!

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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!

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Hey! My name is Sofia Bud, I am 17 years old and I am from "Emil Racovita" National College, Cluj-Napoca.

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Hey! My name is Sofia Bud, I am 17 years old and I am from "Emil Racovita" National College, Cluj-Napoca.

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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

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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

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Ioana Gavrila

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Hello, I am Ana Selejan, 16 years old. I’m from “Emil Racovita” National College

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Hello! My name is Amélie Cannet, I’m 15 years old and I’m from « Val de Durance » at Pertuis, in France.

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Hello! My name is Lisa Coraboeuf I’m 15 years old and I’m from « Val de Durance » in France

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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. 

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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. 

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Amélie Cannet

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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.

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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.

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Ioana Gavrila, Colegiul National "Emil Racovita"

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Hello ! I’m Lana Devals, I’m 15. I’m from « Val de Durance » high school in Pertuis,France.

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Hello! I'm Adrien Siquot, I'm 15 years old.
I'm from " Val de Durance " in France

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hello! I'm Andrea Perrot, I'm 15 years old.
I'm from "Val de Durance" in France

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Hello !
My name is Dorine. I'm 15 years old.
I am from Val de Durance in Pertuis in France.

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Hi, I'm a student from "Val de durance", Pertuis's Highschool, in France. I'm Titouan Marchais and I'm 15 years old.

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Hello!
I'm Hugo and i'm 15 years old.
I'm from Val de Durance in Pertuis in France

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I'm Antonin and i'm 15 years old .
I'm from val de durance in Pertuis in france

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If we cut the kapla (1) in 5, we can see that if we do a regular construction it works with 5 kaplas.

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But with 6 kaplas, it fall.

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Hello, my name is Mateș Ilinca, I am 16 years old. I am from "Emil Racoviță" National College, Cluj-Napoca.

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Hello, my name is Mateș Ilinca, I am 16 years old. I am from "Emil Racoviță" National College, Cluj-Napoca.

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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

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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

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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. 

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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. 

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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.

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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.

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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:)

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Hi!!! My name is Marion Court, I am 15 years old and I am from "Val de Durance" at Pertuis, in France.

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Hello!
My name is Léonie. I'm 15 years old.
I'm from Val de Durance in Pertuis.

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Hello!
I'm Louise and I'm 15 years old. I'm from Val de Durance in Pertuis.

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Hello ! My name is Tom Raffin I'm 15. I'm from Val De Durance high school, in France.

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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 !

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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.

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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 !

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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!

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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!

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With this one we found that it's possible to do it with e^20 blocks and we're working on the demonstration

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With this one we found that it's possible to do it with e^20 blocks and we're working on the demonstration

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Thélu Nathan

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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

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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

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Today we try irregular construction. We found some results.

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Hello, I'm Mélisse and I'm 15 years old. I'm from Val de Durance in Pertuis.

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Hello, I'm Mélisse and I'm 15 years old. I'm from Val de Durance in Pertuis.

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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

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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.

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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.

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Nathan Thélu

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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

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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

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Lazăr Florin

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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.

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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.

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Ioana Gavrila, Colegiul National "Emil Racovita"

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that value n i talked about earlier is going to be useful in calculating the hight of the construction (0.1 * n meters)

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that value n i talked about earlier is going to be useful in calculating the hight of the construction (0.1 * n meters)

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Lazăr Florin

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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.

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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.

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Ioana Gavrila

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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

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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

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Lazăr Florin

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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!

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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!

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Lazăr Florin

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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

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beautiful

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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.

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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.

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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.

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I'm Claire and I'm 15 years old. I'm studying in Val de Durance.

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Today we implemented the formula 1/2 exponent n-1 and found that it was not possible to exceed 1.

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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

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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

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Lazăr Florin

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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

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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

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Lazăr Florin

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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.

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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.

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Lazăr Florin

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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

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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

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Lazăr Florin

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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.

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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.

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Ioana Gavrilă

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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. 

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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. 

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Ioana Gavrilă

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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. 

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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. 

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Ioana Gavrilă

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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.

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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.

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Lazăr Florin

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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.

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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.

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Lazăr Florin

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we tried to do the induction based on surfaces
Sofia Bud

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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.

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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.

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Ioana Gavrilă

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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.

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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.

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Ioana Gavrilă

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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.

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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.

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Ioana Gavrilă

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how would you translate "induction" please (i don't know what it mean )

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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.

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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.

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Ioana Gavrila

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facts

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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.

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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.

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Lazăr Florin

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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.

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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.

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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.

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Review of the three proposed constructions

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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

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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

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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

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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?

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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?

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Ioana Gavrila

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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

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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

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Nathan Thélu

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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 !

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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 !

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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.

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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.

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Laura Sumarriva

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We found this formula to know how to arrange the blocks.

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My name is Alexia Puiac. I am 17 years old. I am from Colegiul National “Emil Racovita”.

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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

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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

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Would you know how to find the limit of a sum ?

Evan Magnier

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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

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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

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Lazăr Florin

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Hi! My name is Ioana Birou. I'm 17 years old and I'm from Colegiul National "Emil Racovita". 

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Hi! My name is Ioana Birou. I'm 17 years old and I'm from Colegiul National "Emil Racovita". 

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We started to find a formula for this construction.
Amélie Cannet

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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 :)

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Presentation to the Val de Durance High School researcher.
Yves PAPEGAY - INRIA Sophia Antipolis

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We found a physic simulator in order to simulate the kaplas. Here it is : https://app.physion.net/

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We found a physic simulator in order to simulate the kaplas. Here it is : https://app.physion.net/

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Robert-Vigani Sacha

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Interactive Physics Simulations | Physion App

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Create interactive physics simulations for fun or educational purposes

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Documents for the common presentation at the Nice Congress

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Documents for the common presentation at the Nice Congress

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Presentations at Marcel Pagnol College

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Presentations at Marie Mauron College