Ask a friend to draw a triangle — the one that comes immediately to their mind’s eye on hearing the word “triangle”. This is an experiment proposed by Eleanor Robson in her article *Words and Pictures*. What are the results? Do we differ from the ancient Mesopotamian scribe … or from each other?

Robson is arguing that even so basic a concept as a triangle is, in part, culturally determined. Are there modern cultural differences in the triangle, or other basic mathematical concepts?

I asked both my younger brothers to draw the triangles and they both drew somewhat equilateral triangles with the base on the horizontal axis. In the article Robson says that the ancient Mesopotamian scribes would draw triangles with the base on the vertical axis. I think that what we see as normal is most certainly a cultural thing because it is what we are taught from a young age and therefore are used to seeing it. Therefore it is “normal” for us to draw a triangle with the base on the horizontal axis. However had we been born in ancient Mesopotamia I’m sure it would have been “normal” for us to draw a triangle with a vertical base. So I think that with most mathematical concepts they are determined culturally. As another example thing about how the Egyptians and Mesopotamians differed in the approach to addition and multiplication.

When I asked my friends to draw triangles, they also drew equilateral triangles with the base on the horizontal axis. Culture definitely plays an important part in this because I think Americans, especially New Yorkers, prefer stability and equality. When a triangle lies flat, people psychologically believe it is stable and will not fall over. And equilateral triangle also has three 60 degree angles, again coming back to the base 60 concept. There are many ways to draw triangles with different angles, but I think culture has led us to prefer dividing things equally. There is noticeable amount of objects surrounding us that show symmetry, whether it is a bridge, the newly created Freedom Tower, or the tables we sit on. As mentioned, I think it is just a matter of what we are used to seeing.

I asked my husband and my friend to draw a triangle both of them drew the modern or equilateral triangles with the base on herizontal axis. I think we are neither different from the ancient Mesopotamian nor from each other, but we may think differently from the ancient Mesopotamian when it comes to certain things in mathematical world. I think the reason why we all draw the same triangle is because of our society. from childhood we are introduce to the equilateral triangle. Therefore it is “normal” for us to draw a triangle with the base on the horizontal axis.

I asked my little cousin,sister and a young adult person. Each of them draw a equilateral triangle,with base on the horizontal or x axis. They said that this is what they learned as kids and this is a triangle.My little cousin said that this is a triangle, because it’s the roof of a house. That was the way the teacher told him. However when I asked this person who only was educated up to 6t

h grade. He is a very old around 65 years old. He draw a triangle with the base on the horizontal triangle but the up side down( \/). He said that the triangle was like “v” with a line in top. ( this person is from Ecuador). Based on this information, I can conclude that some concepts of math are culturally determined. another thing that i would like to add is that some of the different methods ie. division are different from culture to culture. I have learned to do it in a different way and i feel that the way most people do it here is complicated, even though is the universally the same.

I asked my cousin and my friend to draw the triangle. They both draw equilateral triangles with the base on the horizontal axis or x-axis. It is not a surprise, because this is actually the first thing which immediately comes to our minds when we are asked to draw the triangle. We might ask ourself why does it happen? In my opinion, the cultural aspects and our modern education have a great influence on us. This is what we have learned since childhood. However, let’s say, if we lived in Mesopotamia, we would draw the triangle with the base on vertical axis or y-axis. This is just because we would learned like this. The other important mathematical concept is the base 60. For instance, in modern time, 1 hour is equal to 60 minutes, 1 minute is equal to 60 seconds and so on.

I asked my 14 year old cousin to draw a triangle and she asked me what kind of triangle. But I told her any triangle that comes in her mind then she drew an equilateral triangle. And I asked her why she drew that triangle and she said that’s the triangle she learned how to draw and that was the first image that came in her mind. Me personally if they asked me to draw a triangle, I would probably draw a right triangle because I think it’s just easier to draw. Me and my cousin differ because she went to High School in the US and I was taught the French method of Math back in my country; therefore I believe that we differ from each other and that is culturally determined. I believe there are modern cultural differences in the triangle. Each person has a way and method of learning and what we learned since childhood is what we will remember quicker. For example, the way people do their division in the US differ from how we do division in my country.

When I asked my friends to draw a triangle, they drew a right triangle, probably becuase it was the one that they remembered most. In school, I guess the right triangle was stressed a lot. Im not sure what influences there may be but I think it maybe a memory and recall of what was a big topic at school.

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Plimpton 322 consists of trigonometric tables in a very condensed form to economise on cunieform space. The angles are from 30 degrees to 45 degrees, though for cotangents this gives the information for 45 degrees to 60 degrees. The great mystery as to whether the first column does or does not include 1 is explained by sec squared exceeding tan squared by 1, so this column can economically show both. Finding square roots gives secants and tangents both shown in columns. We are not told this but the other degrees can be calculated by the half angle formula cotu +cosecu equals cot u/2.

Further to my comment 0f 20 May 2012, in trigonometry the prefix co in front of sinu, secu and tanu means cosine(90-u), cosec(90-u) and cot (90-u). It therefore follows that if we know the trigonometric ratios for the angles 30 degrees to 45 degrees we can calculate the trigonometric ratios for the angles for 45 degrees to 60 degrees. The half angle formula can then be applied for the rest of the angles from 0 degrees to 30 degrees and from 60 degrees to 90 degrees. Plimpton 322 may contain the elements of a far more sophisticated trigonometric table than is generally recognised by modern users of trig tables and calculators.