Minkowski Distances
This activity belongs to the GeoGebra book GeoGebra Principia.
from an arbitrary point X(x, y) to the origin O.
XO(x,y):= (|x|p+|y|p)1/p
For p=2, we have the Euclidean distance. For p=1, we have the taxicab distance. By varying p, we can observe how the shape of the circle evolves in each case.
- Note: This section arose due to the lockdown declared in Spain in 2020 as a result of the COVID-19 pandemic. The Education Department of Asturias, the region where I worked as a teacher, decided to replace in-person classes with online ones and also decreed the obligation not to advance curricular material in any subject. This led me to look for a field of mathematical exploration beyond the official curriculum but within the reach of 10th-grade students (around 15 or 16 years old). For the students, it was exciting to know that they were investigating a topic virtually unknown to the vast majority of math teachers. Additionally, the change in metric brought about a lot of surprises and questions. A mathematical celebration.
The taxicab distance (also known as Manhattan distance) is especially simple to introduce as a research project in secondary education, as its algebraic form reduces to linear equations.The shape of the circle is significant in any plane geometry. Here, we see the definition of the Minkowski distance
from an arbitrary point X(x, y) to the origin O.
XO(x,y):= (|x|p+|y|p)1/p
For p=2, we have the Euclidean distance. For p=1, we have the taxicab distance. By varying p, we can observe how the shape of the circle evolves in each case. Author of the construction of GeoGebra: Rafael Losada.