Skip to main content

Coastline Paradox

 Ever wondered how the perimeter of irregular surfaces (like coastlines, borders of a fern leaf) are measured and compared? 





For example, let us consider a coastline, you can see that as we zoom in on the picture more irregularities pop up, there is no stage of zooming in where we'll finally reach a straight line. So, if I had to measure the coastline using a 15 cm scale, it'd obviously ignore the small irregularities which lie beyond the scope of a 15 cm scale. If I measure the coastline using a 5 cm scale, then it would accommodate comparatively more irregularities, as a result, the length of the same coastline will be more in this case. This means as the precision of the scale increases the length of the coastline increases. Comparison of coastlines between different regions becomes difficult due to this dilemma. This is known as the 'Coastline Paradox' or 'Richardson effect' and originally the problem was framed as, "How Long is the Coast of Britain?" 

This paradox was explained using the concept of the 'dimension of a fractal'. In simple language, fractal dimension measures the extent to which its border differs from a straight line or it measures its ruggedness. Fractal dimension does not exactly give the length of the coastline but it surely helps to compare how irregular they are. But often we find lengths of coastlines in different situations but none of these is reliable as they do not specify the scale they've used to measure it. 

So, maths has helped us prove that it is not completely possible to find the perimeter of irregular surfaces but one can for sure measure its roughness. 



Labels

Labels:

Comments

Post a Comment

Popular posts from this blog

Prime Numbers in Nature

 Prime numbers are one of the easiest concepts to understand and learn in Maths. But some of the complex problems in Maths belong to this branch. Never would have imagined an application of prime numbers in nature. Thanks to the book 'Weird Maths: At The Edge of Infinity and Beyond' which introduced me to this along with other weird applications of Maths. There's a particular species type of cicadas found in the US called the Magicicada or the 'periodical cicadas' who stay in their larva for 13 or 17 years. Imagine staying inside for over a decade with no connection to the outside world and coming out in the year 2021. People wearing masks walking all around you, smartphones, oh, the shock!🤯 It is the primality of these numbers which interest the mathematicians. The reasons are quite interesting. As the lifecycle of the prey changes, the population cycle (pattern in the population for a period of time) of their predators also vary due to the change in the availabil...
Post a Comment
Read more

Second Phase of Intense Teaching Practice

13th July 2022 The first day was nerve-wracking. It might be the fact that all of us haven't taught a large group of students. During the first internship, most of us had only 8-10 students in a class due to COVID and the idea of teaching a room filled with 50 students seemed to be a challenge. But after meeting the students, eveything seemed to go smooth and it calmed the nerves. The duties were assigned to us by our leader Sreevineetha. I had evening duty, along with Jis and Georgia. We had to make sure that every student gets picked up from school. 14th July 2022 Everyday the teachers have a prayer at the HM's office at 9.10 am. I had lunch duty along with Rubeena, Deepa and Jis.  Today I had to go for substitution at 9A, 10 A, 10 C and 9C. 9A which is an all- boys class with 56 students was difficult to manage. They settled down after I managed to divide them into groups and give them equation related activity. Rubeena and I had gone for substitution at 10 A (all-boys) and ...
Post a Comment
Read more

Sports Meet 2022

 Finally, the day is here. We've been scheduling the sports meet for quite some meet. It had to be postponed due to unexpected rains and finally, it was conducted on Sep 12 and 13 soon after the Onam holidays. We had shotput, javelin throw, 50m, 100 m etc. The involvement and participation in the second years were a little low compared to the first years. Events like shot put, javelin throw, 50 m race etc had good participation. The selection of students for the finals of each event was done on the first day. The finals followed by prize distribution were done on the second day. I was supposed to run the100m race but had to pull out due to previous complications in my leg injury. But I got to participate in the march past which was totally unexpected. By the end of the day, we were dead tired from the scorching sun, but it was all worth it.
Post a Comment
Read more