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:

Comments

Post a Comment

Popular posts from this blog

Day 30 of Online Classes

 Today the day began with Joju sir's class and the physical science association continued with their seminar. We were introduced to the software 'Hot Potatoes', which can be used to make online quizzes. If I had known this earlier I would have used it for 'Mathletics'. The topic was handled by Ancy and Gayathri of Physical science association and they did a great job. Later we had Ancy ma'am's class where we discussed about social change. Ma'am made us switch on our cameras to take a group photo. It felt good too see many faces after a long time.
Post a Comment
Read more

Day 26 and 27 of Online Classes

 On 19th May 2021 the first class was Deepthi ma'am's and we discussed about 'Pedagogy'. Later we had Maya ma'am's class where the social science association continued their seminar presentations via Whatsapp. On 20th May 2021, the first hour was Joju sir's, where the physical science association started their presentation on Open educational resources which is the continuation of my seminar topic CC license. Sir, ended the class with the story of the Dodo bird found on the islands of Mauritius and the dodo tree or tambalacoque. Later, we had Ancy ma'am's class where we discussed the role of education in democracy.   
Post a Comment
Read more

A New Phase

 This week marked the beginning of teaching practice. St Mary's, Pattom is the school assigned for me. It's going to be a great opportunity and experience for all of us.The internship was supposed to start on 5th January but it was delayed by a day due to an unexpected holiday.  6th Jan 2022, It was the first day of our internship and to be honest I was excited and nervous at the same time. I had the first hour at 9J1 which was utilised to show a video on 'Social Media and its Effects'. The video was shot and shown as a part of a government initiative to create awareness of the positive and negative effects of social media. I couldn't take a class, but I got to be the tech support for the teachers. This helped me get rid of that unnecessary stress. But I had another period at 9I1 and I used this period to get to know the students, their previous knowledge etc. and also brushed some of the previously taught topics. 7th Jan 2022, Today the second batch attended school...
Post a Comment
Read more