Architect

Associate Professor Norman Wildberger, of the University of New South Wales in Sydney, Australia, says his theory of "rational trigonometry" is more like algebra as you can plug numbers into an equation and get an accurate result.
"We're going to look at trigonometry in a new way," says Wildberger. "We're going to leave sines and cosines to the circular motion part of mathematics and not force it on triangles."
New Concepts
The key purpose of trigonometry is to understand the relationships between the corners and sides of triangles. It is used in areas like surveying, engineering and construction today. An angle can be calculated using an equation that relates the corners of a triangle to the length of the side opposite it. But Wildberger says that distance is not the best way to measure the separation of two points and angle is not the best way to measure the separation of two lines. Instead of distance, Wildberger's trigonometry uses a concept called "quandrance", the square of distance.Instead of angle, he uses the concept of "spread", calculated by dividing one quadrance by another. The spread between two lines is a number between 0 (representing parallel lines) and 1 (representing lines at right angles). Wildberger says it would be possible to make a new protractor that measures spread instead of angle. You would then plug the values for the quadrance and spread into his set of equations.
More Accurate
What's better about the system, says Wildberger, is that all the terms in the equations can be calculated exactly, or are "rational", hence the term for his new theory, "rational trigonometry". But sine, cosine and tangent, are usually only approximated, he says, making them "transcendental functions". This means that any complex calculation using classical trigonometry could result in a significant accumulation of errors. Wildberger says he hopes that "rational trigonometry" will provide high school students with a simpler way of thinking about triangles that is both more accurate and easier to carry out.

Thinking about architect as an occupation?

What are the Educational Requirements for an Architect?

All States and the District of Columbia require individuals to be registered or licensed before calling themselves architects and contracting to provide architectural services, according to the U.S. Bureau of Labor Statistics. Before being licensed, Architecture school graduates generally work in the field under direction of an architect who is licensed and who takes legal responsibility for any work that is done. Architects must be licensed before they can practice. In order to get a license: 1) You need a degree in architecture. Courses include architectural theory, building design, math, and science. 2) You must finish an internship. 3) Finally, you must pass all sections of a license exam. Architects sometimes take new classes to keep their skills fresh. Architects must be able to visualize things and communicate well visually. Art classes are very helpful in doing this. Speaking, writing, and creativity are also important. Architects should be computer literate.

What are the Licensing Requirements for an Architect?

A professional degree in architecture, practical training or internship, and passing all divisions of the ARE -Architect Registration Exam are licensing requirements. Most states demand that the professional degree in architecture is from one of the architectural school that have programs accredited by the National Architectural Accrediting Board. Graduation from a program that is not NAAB accredited may meet the licensing educational requirement in a few states since state boards of architectural registration set their own standards. The majority of architectural programs are 5-year Bachelor of Architecture degrees for students entering university directly from high school or with no previous training in architecture.

What is the Occupational Outlook for an Architect?

Architects held about 129,000 jobs in 2004, according to the U.S. Bureau of Labor Statistics. Most jobs were in small architecture firms. About 1 in 4 was self-employed. This means they practiced as partners in a firm or on their own. Some worked for builders or government agencies. Approximately 3 out of 5 jobs were in the engineering, architectural and related services industry - mostly in architectural firms that have fewer than five workers. BLS expects the number of jobs for architects to grow about as fast as the average for all occupations through 2014. Despite this growth, however, new architects face competition. This job attracts many people, so there are lots of applicants for openings. Applicants who gained experience working for an architectural firm while in school have a competitive advantage. Those who know about computer-aided design and drafting technology also have a better chance to get a job.How much does this job pay?The middle half of all architects earned between $46,690 and $79,320 a year in 2004. The lowest-paid 10 percent earned less than $38,060. The highest-paid 10 percent earned more than $99,800 a year.

French mathematician and physicist Joseph Fourierused a series of sums to form this:

Where each of the squares ( ) is a different number, and one is adding infinitely many terms. Fourier used these for studying heat flow and diffusion.

Meteorology

Atmospheric science is the study of the atmosphere—the blanket of air covering the Earth. Atmospheric scientistsare also known as meteorologists and study the atmosphere’s physical characteristics, motions, and processes, and the way in which these factors affect the rest of our environment. They most often are known for predicting the weather, but addition to that, they also attempt to identify and interpret climate trends, understand past weather, and analyze today’s weather. Weather information and meteorological research are also applied in air-pollution control, agriculture, forestry, air and sea transportation, defense, and the study of possible trends in the Earth’s climate, such as global warming, droughts, and ozone depletion. Based on this, it is easy to conclude that meteorology is a very important profession that is not restricted to a particular region, although different climates would have very different uses of the field.

Applying Trigonometry

If you know the altitude of the clouds, it is possible using simple trigonometry to calculate the speed of the winds carrying them along. When directly overhead, an object at 30,000 feet that traverses an arc of 30 degrees of the sky will travel about three miles. If it travels this distance in three minutes, the speed would be 60 mph , which is typical for winds at 30,000 feet.

Required Education

About 37 percent of atmospheric scientists are employed by the Federal Government; most of these work in the National Weather Service.

Minimum Required Education

A bachelor’s degree in meteorology is the minimum educational requirement. Although positions in operational meteorology are available for those with only a bachelor’s degree, obtaining a second bachelor’s degree or a master’s degree potentially opens up opportunities for higher positions and, therefore, a greater salary. A master’s degree is necessary for some positions, and a Ph.D. degree is required for most basic research positions.

Additional Training

The American Meteorological Society (AMS) offers professional certification for consulting meteorologists, administered by a Board of Certified Consulting Meteorologists. Applicants must meet formal education requirements, pass an examination to demonstrate thorough meteorological knowledge, have a minimum of 5 years of experience or a combination of experience plus an advanced degree, and provide character references from fellow professionals. In addition, AMS also offers professional certification for broadcast meteorologists.Atmospheric scientists have favorable job prospects, but opportunities as weather broadcasters are rare and highly competitive.