Comparison
We have compared our project about maths in architecture to ‘het college Weert’ and ‘Bal Bharati Public School in Rohini’. The topic of the school in Weert was impossible constructions and the topic of the school in Rohini was monuments. And we talked about bridges. There is a lot of variety in our topics. We used more formulas than the other school in our opinion. And they kept it more general and didn’t use formulas, but looked for patterns (Indian school) and for solutions (Dutch school). We thought it was nice that we have done our research in a completely different ways and we are happy with the results. Reflection We reflect on this project as fun and with good co-operating. At first we divided the tasks. Carlijn and Veerle were to investigate which bridge is the strongest. Isabelle and Maaike were to found out everything about the Da Vinci bridge and Joni was going to apply several formulas on a famous bridge.Everyone was satisfied with her task, but it was a bit unclear to us how we had to upload all of our gathered information,what the deadlines were and what we had to discuss with the Indian school. So we got a bit confused there. But all-in all it worked out just fine and we are pleased how it worked out. (again the outlay order switched, my apologies) |
We are Joni, Maaike, Carlijn, Veerle and Isabelle
and our subject is maths in architecture!
Joni. (Groupleader)
Hello, I’m Joni and I’m 14 years old.
My hobbies are dancing and meeting up with friends.
Veerle.
Hello, I’m Veerle and I’m 14 years old.
My hobby is playing korfbal.
Isabelle.
Hello, i’m Isabelle and I’m 14 years old.
My hobbies are playing soccer,
reading books and meeting up with friends.
Carlijn.
Hello, I’m Carlijn and I’m 14 years old.
My hobbies are playing tennis and reading books.
Maaike.
Hello, I’m Maaike and I’m 14 years old.
My hobby is playing volleyball.
Hello, I’m Joni and I’m 14 years old.
My hobbies are dancing and meeting up with friends.
Veerle.
Hello, I’m Veerle and I’m 14 years old.
My hobby is playing korfbal.
Isabelle.
Hello, i’m Isabelle and I’m 14 years old.
My hobbies are playing soccer,
reading books and meeting up with friends.
Carlijn.
Hello, I’m Carlijn and I’m 14 years old.
My hobbies are playing tennis and reading books.
Maaike.
Hello, I’m Maaike and I’m 14 years old.
My hobby is playing volleyball.
We have chosen to do this particular subject of mathematics, because we were wondering how all the beautiful creations we see in daily life are actually made. We think that when you have a look around in your enviroment many things or maybe even most things are a part of architecture. Of course, architecture is such a big subject that has many interesting aspects, but we can’t cover it all. That’s why we have chosen to do bridges, we think they are very important, because how could we transport easily/quick without them and how are they built?
Evidence of communication:
How do you generate a formula for the Sydney Harbour bridge?
In order to create a formula for a bridge with an arched shape, you have to use the form:
Y=a(x-d)(x-e)
D and E represent the points at the x-axis where the bridge passes trough.
When you have a look at the Sydney Harbour Bridge, you can see that (246,0) and (1067,0) are the two points that cross the x-axis.
When fillingin the points the formula results in: Y=a(x-246)(x-1067)
If you take a look at the bridge you’ll see that (-80,-100) is a point on the graph. This point is needed to create the formula (or any other point on the graph). -80 should be filled in for x and -100 can be written down as the outcome.
:
A(-80-246)(-80-1067)
A * -326 * - 1147= 100
373.922a=-100 —> a=-100 : 373922 = 0,00026744
The formula of the bridge will result in : 0,00026744(x-246)(x-1067)
In order to create a formula for a bridge with an arched shape, you have to use the form:
Y=a(x-d)(x-e)
D and E represent the points at the x-axis where the bridge passes trough.
When you have a look at the Sydney Harbour Bridge, you can see that (246,0) and (1067,0) are the two points that cross the x-axis.
When fillingin the points the formula results in: Y=a(x-246)(x-1067)
If you take a look at the bridge you’ll see that (-80,-100) is a point on the graph. This point is needed to create the formula (or any other point on the graph). -80 should be filled in for x and -100 can be written down as the outcome.
:
A(-80-246)(-80-1067)
A * -326 * - 1147= 100
373.922a=-100 —> a=-100 : 373922 = 0,00026744
The formula of the bridge will result in : 0,00026744(x-246)(x-1067)
Interview with mr. Lauwers, an architect
43 years old. 1. How do you measure a room? For what do you use these measurements? When I measure a room, I always measure it myself, because a house is rarely built completely on the instruction drawings. I measure it with a laser rangefinder. That’s a tool where you can measure the whole house exactly by using lasers. Then I always make a 3-D drawing from it so I know the exact measurements. Then I can start designing the house. 2. Do you also use formulas to calculate something? Yes, when I for example need to determine a roof slope, I always use the formula angle= adjacent side / opposite side 3. what do you do with maths in your job? I do a lot of maths in my work. For example to make calculations of strength or calculations so you can see if enough daylight comes in. 4. Could you tell me what you have to do when you’re an architect? I design houses for private and I also work it out technically so the builder knows exactly how it has to be built and with which materials. I also make sure the builder has the licence applications needed. |
Interview with Maaike’s dad. He is application Engineering Manager and he is 46 years old.
1. How does maths involve in your work? I use maths for several things during the day: - Calculate the content of a product silo - Calculate the sales price for a project based on a certain percentage we want to meet - Calculate the angle of conveyors for transporting bags. Sometimes the space is too narrow to install our machines and then the conveyor will be steeper, but too steep is not good. - Calculate the capacity of a dosing screw (how many litersper sec --> how many kg per sec -> how many kg per bag —> how many bags per hour - Statistics to check how many quotes are made, are on-time, at what price….. 2.How does maths involve in your life? Not that much mostly you use arithmetics, to quickly calculate the price you need to pay during shopping 3. What or which part do you like most about maths? I like statistics the most. In a lot of data you are able to find certain relations and base your next action towards the goal you need to achieve. 4. Were you good at maths? Till the 3rd grade I was not that good in maths. I survived barely with a 6. When I choose for maths A, I developed myself and was quite good in math. I did not have to learn for my final exams, I had already a 9 as average and I was sure in would pass. 5. How was maths in school back in the times? Boring, but happily enough the teacher made the difference. 6. Do you know the Pythagorus theorem? If so, what is it used for? Yes a2 + b2 = c2. You can calculate lengths, heights of triangles |
Interview with Carlijn's dad. He is 45 years old.
What do you do as a job? - I’m a forest manager. This means I’m busy with all kinds of maths, such as estimates, areas and volume in forest management. What would be a very mathematical trick in your job? - It is calculation to calculate the height of a tree by hand. We than use two sticks of the same length, they form a 90 degrees angle upwards = _|. If you stand at a distance of X meters from the tree and you hold the lower stick close to your eye, you will see that the tree is as tall as the upper stick. If you draw this it will look like this: Now you might see that it are two triangles which have the same ratio. This is than how you calculate the height, because the height will be the same as X (which can be measured). You talked about areas, what do you so with them? - I calculate areas of for exampleponds/lakes. For all kinds of shapes, we have formulas which differ. Our most used is a square plus triangle: AxB+1/2xC=area |
Interview with Veerle's dad, an accountant.
Do you know the pythagoream theorem? Yes, it is ab2+bc2=ac2 What is your job? I am an accountant. I calculate the costs of a company. I work with excel. I put the formula in excel, which calculates everything for me. What kind of math did you do at school? I did a kind of math with a lot of percentages and statistics. I like the statistics the most, because you can use the information you calculate for a certain goal. Were you good at math in the third grade? No, I was quite bad at math. I didn't understand most formulas, so I chose for statistics. At my final exam I scored a 4.5/10 The Da Vinci Bridge
Leonardo designed this bridge while he was under the patronage of Cesare Borgia. Borgia employed Leonardo as his military engineer, in turn, Leonardo would design and build magnificent machines of war. One such machine was this bridge. Its simplicity and genius cannot be underestimated. It requires no specific skills to manufacture the parts, apart from a few men that are handy with an axe. It can also be carried by some men into any battlefield. It requires no nails or ropes to hold it together – the bridge is self-supporting. We have found some difficulties constructing the bridge, because it isn’t that solid whole the time. After some practice we got the hang of it and it went well. By enclosing the sticks in the form of a cross the bridge stays impact and by continuing this process you can go on as long as you want. source: http://www.leonardodavincisinventions.com/leonardo-da-vinci-models/leonardo-da-vincis-self-supporting-bridge/ |
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Which bridge is the strongest?
We built several bridges and tested if they were strong and could hold a bit of pressure. The most important thing we discovered was that indeed triangles are much stronger than squares.
1. The first bride we tried was one completely made out of squares.
It was even difficult to build because it didn’t want to stand straight up. If you toughed it, it would immediately collapse. This one was absolutely the least strong.
2.
The second bridge we made was one with 2 out of 4 sides made of triangles.
It is stronger than the first one but it will still collapse towards one side, this is because the squares can’t keep the sides properly together. You can also see on the picture that is looks a bit unstable.
3.
Thirdly we built a bridge with 2 out of 3 sides made of triangles.
This bridge was very stable and strong and could handle much pressure. The thing that played a role here is that the material couldn’t handle the pressure.
4.
At last we built a structure, not really a bridge, to see if a structure with only triangles would even be stronger.
You could actually throw with this object without breaking the structure. This shows that was very strong.
Our conclusion is that the more triangles in comparison the stronger a bridge or object. That is why you see many triangles in bridges and other architecture
We built several bridges and tested if they were strong and could hold a bit of pressure. The most important thing we discovered was that indeed triangles are much stronger than squares.
1. The first bride we tried was one completely made out of squares.
It was even difficult to build because it didn’t want to stand straight up. If you toughed it, it would immediately collapse. This one was absolutely the least strong.
2.
The second bridge we made was one with 2 out of 4 sides made of triangles.
It is stronger than the first one but it will still collapse towards one side, this is because the squares can’t keep the sides properly together. You can also see on the picture that is looks a bit unstable.
3.
Thirdly we built a bridge with 2 out of 3 sides made of triangles.
This bridge was very stable and strong and could handle much pressure. The thing that played a role here is that the material couldn’t handle the pressure.
4.
At last we built a structure, not really a bridge, to see if a structure with only triangles would even be stronger.
You could actually throw with this object without breaking the structure. This shows that was very strong.
Our conclusion is that the more triangles in comparison the stronger a bridge or object. That is why you see many triangles in bridges and other architecture