Tangled Triangles

Ph.D.
Math Problem
Science
Pages 4 (1004 words)
Download 0
Two students are discussing how to find the biggest value of the area: perimeter ratio for triangles. One of them suggests that this can be done with measurements of 40, 60 and 80- but forgets to say what units were used, and whether they were angles or sides.

Introduction

The ancient Greeks were aware of this and often used this information in their day-to-day life. Perhaps it all started with the 'Dido's fix' in eighth century BC. However, in most of the cases, these observations were stated with any formal proof backing them. Whether it is a bubble taking a spherical shape to minimize surface energy or the hexagonal shape of honeycomb to maximize honey storage, it has only fuelled the mathematician's interest in questions of Maxima and Minima. Starting in the seventeenth century, the general theory of extreme values Proof: To find out the triangle which gives the biggest value for the area: perimeter ratio, we can either try to minimize the perimeter keeping the area consta ...
Download paper
Not exactly what you need?

Related papers

Mathematical Tasks
A mathematical task like the one below entails many more mathematical objects apart from geometry because algebra can also be involved.…
Maths investigation
1/3*1/3=1/9. Thus the number of sides is increased by 4 times i.e. 4*12=48. Length of the side is decreased by 3 times. The perimeter is calculated directly as number of sides in this stage multiplied by the length of the side in the same stage i.e.48*1/9. Now each side in the previous stage gives rise to one equilateral triangle in this stage with side 1/3 of the side in the previous stage…
Tangled Triangles
The ancient Greeks were aware of this and often used this information in their day-to-day life. Perhaps it all started with the 'Dido's fix' in eighth century BC. However, in most of the cases, these observations were stated with any formal proof backing them. Whether it is a bubble taking a spherical shape to minimize surface energy or the hexagonal shape of honeycomb to maximize honey storage,…
Global Warming Book Report/Review
While it is increasingly accepted by a growing number of policy makers that action needs to be taken immediately to address climate change, it is politically difficult to do so when the impacts, in most parts of the world, are still insignificant. This is a classic 'Catch 22'. When it is possible to take decisive action to prevent catastrophe, the lack of major impacts justifies delays; but when…
Models of Object Recognition
This is simply 'object recognition'. When a lion approaches us, we realise through prior knowledge that the animal is known to be ferocious, dangerous and sometimes doesn't hesitate to kill. With this information we are able to make instant decisions as to the next course of action. A meal at a dinner table tells us it is edible and we can approach it. This 'spatial localisation' is the…
Context and Discourse
Such technicians proceed to use this information to create context-aware software. Close attention to these several definitions and explanations might, however, reveal a common ground upon which a universal concept of context might be built. Though context is often used and understood, it is such a broad and encompassing term that it can hardly be properly defined in a sentence or two. Though it…
Triangulation in Geometry
More specifically, it can be defined as the underlying space of a simplicial complex. Here, a polyhedron can be viewed as an intersection of halfspaces (Webster 1994).…