# Most stable shape- triangle

## Introduction

## Description

**F****=**

*Where*

**ma**

*F*is net force,

*m*is the mass and

*a*refers to acceleration.

To ensure the swing does not fall off, the net force in a vertical direction should be zero.

2. For economic reasons: since the triangle obviously has only 3 sides, it requires little material to make a support, thus minimizing the costs.

Overall, a triangle is the simplest geometrc figure that will not change shape when the lengths of the sides are fixed. In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.

Actually, The Mathematical Bridge between two parts of Queens' College, Cambridge also demonstrates a triangulated structure. It is made up of a series of timber tangents joined together to make it rigid.

**
**In architecture, this technique is called

**tangent and radical trussing.**

By definition, a truss is a structure consisting of triangular unit(s) constructed with straight members whose ends are connected at joints referred to as nodes.

A tetrahedron-shaped base in a flying fox is a simple space truss. It contains six members joined at 4 points.

More examples in our city:

This is an example of a simple truss.

*m*is the total number of members,

*j*is the total number of joints and

*r*is the number of reactions, e.g.

*r*=3 in a 2-D structure.)

**Demonstration:**

First of all, we need to accordion fold an A4 sheet of paper.

Use two books as supporters and put the paper on top of them.

Now, we put a load on it.

Surprisingly, the A4 paper is able to support two books which are far heavier than its own weight.

Some buildings are built with more than the minimum number of truss members required. Therefore, they do not not collapse easily even if some members are damaged.

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