Trigonometry: Bridging Architecture and Electric Science

Introduction

My interest in Architecture as a mathematician sparked in the first place whenever I cross a bridge either riding my bicycle or driving my car. How could a structure being held with such large weight of vehicles and people crossing over it on a daily bases, besides the shape that a bridge is which looks like the diameter of a circle linking two different ends with each other. Moreover, I had a thought how electricity is generated and consequently being transferred to other places along with transformers which are responsible for the electric current to flow, and thus I want to observe how trigonometry contribute in this.

Math is the structure of all science sections, and the reason behind nations development. Trigonometry simply means triangle equations (that is where the trial originates). It is a study of mathematical relationships involving the distances, heights, and angles of various triangles. The area originated from Geometry applications to astronomical studies during the 3rd century BC.

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Trigonometry extends its applications to different fields, such as architects, surveyors, astronauts, physicists, engineers and even investigators of the crime scene. This science includes what is called functions or the trigonometrical ratios, which are basically the following:

Sin(θ)= OPP/HYP

Cosine(θ)= ADJ/HYP

TAN(θ)= OPP/HYP

Diagram 1

SImply, trigonometry measures the triangle components. Such as:

The three sides

The three angles

Moreover, the relation between the sides and angles of the triangles forms the basis of trigonometry. What makes triangles exclusive to be a use for trigonometry measurement, in the right angle triangle.

When one angle increase, such as the hypotenuse. Other angles increase in the same ratio, and the same applies when a side increase or decrease. And that has been proved by Pythagoras theorem, which is the example bellow

Triangle 1: Triangle 2:

Sin(36.86)= ⅗ Sin(36.86)=6/10

Cosine(36.86)=⅘ Cosine(36.86)= 8/10

Tan(36.86)=¾ Tan(36.86)= 6/8

Yet unfortunately, most of us do not understand the following points:

What is the idea behind Trigonometry?

What are the trigonometry applications and uses?

What is the importance of this type of science?

Why this science is prominent to architecture?

Research Question:

What are different aspects of trigonometry used in the real world?

Rationale:

My interests first sparked at these two applications of Trigonometry, the Architecture and Electric Science.

Trigonometry and Architectures

One of the most common applications of trigonometry is in architectures, since it has various uses such as roofs, bridges, buildings. In Addition, the construction sector. Architects have been used more commonly, due to it is more precise in terms of measurements than other tools which might include some human errors and etcetera. Furthermore, trigonometry took a large part of the truss system construction.

A truss is a structural component made mostly from straight metal or timber parts to form a series of triangles lying in one plane. Tresses are used in a broad range of buildings mainly where there is a requirement for very long spans, such as sport stadia roofs and aircraft hangers. Moreover, trusses are even used to carry heavy loads and sometimes carry large structures. The hypotenuse of a triangle is what creates such a strong structure due to its ability to cross and support beams and columns.

A truss provides a solid form with the component parts strained mainly in axial tension or compression that can withstand a significant external charge over a large span. At truss joints or panel dots, the individual pieces intersect. The linked pieces which form the top and bottom of the truss are called the top and bottom chords, respectively. The sloping, vertical pieces that connect the chords are collectively referred to as the truss web.

Trusses were probably first used during the early Bronze Age, around 2500 BC, in primitive lake dwellings. The first trusses were made of timber. The Romans made extensive use of trusses in roofing, and in the European Middle Ages, trusses were used for various building purposes. The I QuattroLibri dell Architettura (1570; Four Books on Architecture), by Andrea Palladio, included designs for timber trusses. In the early 19th century, a significant impetus to truss construction came in the development of covered bridges in the USA. Steel for the railroad truss bridges replaced cast iron and wrought iron. The two most widely used structures are the Pratt and the Warren; in the former, the sloping network members are parallel to one another, while in the latter, they differ in slope direction. Trusses are also used in many types of machinery, such as cranes and lifts, and in the wings and fuselages of aircraft.

An example of Trigonometry in Architects is escalators, Escalator, moving staircase used as transportation in subways, buildings, and other mass pedestrian areas, between floors or levels.

The inclined belt, invented by the United States Jesse W. Reno in 1891, provided transport for passengers sitting on cleats attached to the belt, which was inclined at an angle of 25 °; the handrail was fixed, but an improved version with a rotating handrail was introduced the same year.

The term escalator was first applied to a travelling stairway demonstrated at the 1900 Paris Exposition. Originally a trademark of Otis Elevator Company, in 1949 the word was adjudicated as having become public property by popular use.

Modern escalators are typically inclined at 30 °, restricted to about 60 feet (18 m), with an elevation of about 12 feet (3.5 m) from floor to floor. They are powered by electricity; Driven by a chain and a sprocket, and supported by two tracks in the proper plane. As the treads approach the landing, they pass through a comb device; if an object becomes jammed between the tread and the comb, a deflection switch is actuated to cut off power.

Trigonometry and Alternative electricity

The alternative electricity is a form of electricity which we use on a daily basis in our life, and can be illustrated in the following form:

Moreover, it is a figure of sine function altered over time. And the function form is conveyed in the diagram below:

The alternating current is generated by the electrical generator which converts the mechanical energy from the conventional engine to a electrical energy, by rotating the electrical coils within a magnetic field.

For physics, trigonometry is used to locate vector components, to model wave mechanics (both physical and electromagnetic) and oscillations, to sum up, field strength, and to use dot and cross-products. You even have a lot of use of trigonometry for projectile motion. The electromagnetic wave which presents in the diagram above is illustrated by the following forms the electromagnetic wave equation takes the form.

Reflection

Through this investigation, there were some obstacles in my research, since the sources that I extract some information from must reliable and surely true, thus this is to consider this point as a limitation to my investigation. An advantage of this topic to investigate is that it has many applications for further investigation and observation.