Today in History – December 21, 1807 – Fourier introduces his series at the Paris Institute. Joseph Fourier’s memoir, On the Propagation of Heat in Solid Bodies, was read to the Paris Institute. It introduced the expansion of functions into trigonometric series which are now called Fourier series.

The Fourier series allows periodic functions to be represented as a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. The weights, or coefficients, of the components, arranged in order of increasing frequency, form a sequence (or function) called Fourier series. Fourier analysis provides a frequency domain representation of a time domain function. The mapping between the two functions is one-to-one, so the transform is reversible. A common visualization of this transformation is the audio equalizer, which is a dynamic representation of a time signal converted to the frequency domain. An audio spectrum of both time and frequency is shown below.

Preliminary work by Madhava, Nilakantha Somayaji, Jyesthadeva, Leonhard Euler, Jean le Rond d’Alembert, and Daniel Bernoulli would serve as the foundation for Fourier’s work. He applied his studies of trigonometric series to a solution of the partial differential heat equation to produce the series below:

Fourier’s initial series lacked the precision of a function, and Dirichlet and Riemann would later express the series as a formal integral.

Fourier series applications include electrical engineering, vibration analysis, acoustics, optics, signal and image processing, and data compression. Using the tools and techniques of spectroscopy, astronomers can deduce the chemical composition of a star by analyzing the frequency components, or spectrum, of the star’s emitted light. Similarly, engineers can optimize the design of a telecommunications system using information about the spectral components of the data signal that the system will carry.

For more information, see the Engineering Pathway‘s resources on Fourier and the Fourier series For related educational resources, visit the Electrical Engineering Education disciplinary community.

Today in History – October 23-24 – TRON Legacy Exhibit at the National Science & Engineering Festival.

The National Academy of Engineering (NAE) has teamed up with Walt Disney Studios to co-create an interactive exhibit in Tent 102 at the USA Science & Engineering Festival Expo, which will take place on the National Mall in Washington, D.C., on Oct. 23 and 24 from 10 a.m. – 5:30 p.m. each day.  The hands-on experience blends themes from the upcoming major motion picture TRON: Legacy with the NAE’s Grand Challenges for Engineering.

Exhibit-goers will be transported into the digital world of TRON: Legacy and examine where movie fantasy and reality intersect.  Visitors can try 3-D scanning and see how it’s bringing the real and virtual worlds closer together.  They’ll get a chance to do brain surgery on a computer-generated replica of a real brain, and experience a trip into the TRON: Legacy digital grid through an incredible 3-D light painting activity created especially for this exhibit. The NAE worked with Disney Imagineering research scientist Lanny Smoot (upper right photo) to develop the interactive demo.

TRON: Legacy is the stand-alone sequel to the 1982 motion picture TRON.  Both star Jeff Bridges as software engineer and video game developer Kevin Flynn, who was digitized by a laser and transported into a world of computer games in the original film.  In TRON: Legacy, Flynn’s son Sam finds himself in the digital realm where his father has lived for the past two decades.  The film, in theaters nationwide on Dec. 17, 2010, involved cutting-edge movie technologies, including one that allows Bridges to act as his younger self.

“Engineering is woven into the very fabric of TRON: Legacy. The story is rich with themes about technology and its evolving relationship with humanity in an increasingly digital world,” said co-producer Justin Springer.  “The line between science and art is blurring more than ever.  And some of the most talented artists in modern film making are engineers, mathematicians, architects, and computer programmers.”

An international committee of some of today’s most accomplished engineers and scientists determined the NAE’s Grand Challenges for Engineering.  They identified 14 potentially “game changing” goals for helping people and the planet thrive in the 21^st century that include enhancing virtual reality; engineering better medicines; advancing personalized learning; engineering the tools of scientific discovery; and reverse engineering the brain.

For more information, see the Engineering Pathway’s resources on the inaugural USA Science & Engineering Festival and the NAE Grand Challenges. For related educational resources, visit the engineering education and the computer graphics & visualization disciplinary communities.

Also on this date on October 23, 1819, the first boat passed through the Erie Canal. On October 24, 1861 the transcontinental telegraph line was completed.

Today in History – March 14, 1987 – First Pi Day is celebrated.  3/14 (3.14) was chosen by physicist Larry Shaw of the Exploratorium Museum in San Francisco to be celebrated as Pi Day.

For more information, browse the Engineering Pathway’s educational resources on Pi Day and other irrational numbers.

Today in History – January 26, 1697-  Isaac Newton solves Bernoulli’s brachistochrone problem, inventing the “calculus of variations”. The story goes that Jean Bernoulli gave Isaac Newton a challenge solve the following problem in six months:

We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination in the briefest time.

Rather than take 6 months, Newton is reported to have solved the problem the next day. However, the solution, which is a segment of a cycloid, was solved, in part, by Leibniz, L’Hospital, Newton and the two Bernoullis. In fact, there appears to have been quite a lively, and in some cases bitter, debate about the fine points of the solution. Regardless, the challenge was to provide the seed for further development of the theory of calculus of variation used in a wide range of engineering problems, such as optimal control and optimization.

For more information, see the Engineering Pathway’s resources on Isaac Newton, the Brachistochrone problem and calculus of variations.

Also on this date in 1905, Cullinan Diamond (“Star of Africa”), the largest diamond ever found, is unearthed. On January 26, 1926, Scottish Engineer John Baird gives first public demonstration of television in London. And in 1992, Americans with Disabilities Act went into effect. Check out the Engineering Pathway’s resources on teaching and learning for persons with disabilities.
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Today in History – December 13, 1928 – Today is Clip-on Tie Day. That’s right, on this day, 79 years ago, someone (and I couldn’t find out who) invented the clip-on tie. This fine fashion accessory often gets a bad wrap. People belittle it as the tie for people that don’t know how to tie a tie themselves.

If you are somehow unfamiliar with what a clip-on tie is, it is essentially a bow tie or four in hand tie which is permanently tied into its knot with a dimple just below the knot. Instead of looping around the neck, this tie is simply fixed to the front of the shirt collar with a metal clip. Though it doesn’t look as much like a real tie to fool everyone, and may accidentally come off with a too-hard tug, many people use clip-on ties every day.

The fact that a clip-on tie is likely to come off should it be tugged is actually a wonderful safety feature, especially for people such as police, paramedics, and engineers. Many of these occupations require personnel to use clip-on rather than full ties. Others might be mocked for wearing clip-ons because they don’t know how to tie a tie, or because they feel it is less restrictive, but the good old clip-on redeems itself by helping many wearers stay out of harms way. So here’s to that mysterious inventor of the clip-on tie. Harrah!

Meanwhile, to help make sure you’re never caught out not knowing what knot to tie, check out the Engineering Pathway’s resources on knot design and mathematics.

Have you developed courseware – interactive websites, simulations, tutorials, case studies, software environments or tools – designed to enhance engineering education? We want to see it! Submissions due July 17, 2009.

The Premier Award for Excellence in Engineering Education Courseware, hosted by the Engineering Pathway, is open to a wide range of submissions of high-quality, engaging, non-commercial learning innovations designed to enhance engineering education. Submissions for 2009 are due by July 17, 2009, and the Premier Courseware of 2009 will be announced at the Frontiers In Education Conference to be held October 18-21 in San Antonio, Texas. More details on the Premier Award and current and previous winners can be found on the Engineering Pathway at: http://www.engineeringpathway.org/premier/.

Check out our prior Premier Award winners. The 2008 Premier Award for Excellence in Engineering Education Courseware was awarded to Richard Anderson, Ruth Anderson, Natalie Linnell, Craig Prince and members of the development team from the University of Washington for Classroom Presenter.

Classroom Presenter is a Tablet PC-based interaction system that supports the sharing of digital ink on slides between instructors and students. Classroom Presenter enables the flexible delivery of lecture content and can increase student engagement and understanding of material. When used as a presentation tool, Classroom Presenter allows the integration of digital ink and electronic slides, making it possible to combine the advantages of whiteboard style and slide-based presentation. The ability to link the instructor and student devices, and to send information back and forth provides a mechanism for introducing active learning into the classroom and creates additional feedback channels.

Richard Anderson is a professor of Computer Science and Engineering at the University of Washington and also serves as Associate Chair of educational programs. He won the 2007 UW Faculty Innovator for Teaching Award. Ruth Anderson teaches Computer Science at the University of Washington.  Natalie Linnell and Craig Prince are both PhD students at University of Washington working on educational technology with Richard Anderson.

The Engineering Pathway (www.engineeringpathway.org) is a portal to high-quality teaching and learning resources in applied science and math, engineering, computer science/information technology and engineering technology, for use by K-12 and university educators and students. Engineering Pathway is the engineering education “wing” of the National Science Digital Library (NSDL) at www.nsdl.org.

The Engineering Pathway also hosts Engineering Education communities in all ABET-accredited computing and engineering disciplines as well as emerging new interdisciplinary communities.

Today in History – March 14, 1987 – First Pi Day is celebrated.  3/14 (3.14) was chosen by physicist Larry Shaw of the Exploratorium Museum in San Francisco to be celebrated as Pi Day.

For more information, browse the Engineering Pathway’s educational resources on Pi Day and other irrational numbers.

Today in History – January 26, 1697-  Isaac Newton solves Bernoulli’s brachistochrone problem, inventing the “calculus of variations”. The story goes that Jean Bernoulli gave Isaac Newton a challenge solve the following problem in six months:

We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination in the briefest time.

Rather than take 6 months, Newton is reported to have solved the problem the next day. However, the solution, which is a segment of a cycloid, was solved, in part, by Leibniz, L’Hospital, Newton and the two Bernoullis. In fact, there appears to have been quite a lively, and in some cases bitter, debate about the fine points of the solution. Regardless, the challenge was to provide the seed for further development of the theory of calculus of variation used in a wide range of engineering problems, such as optimal control and optimization.

For more information, see the Engineering Pathway’s resources on Isaac Newton, the Brachistochrone problem and calculus of variations.

Also on this date in 1905, Cullinan Diamond (“Star of Africa”), the largest diamond ever found, is unearthed. On January 26, 1926, Scottish Engineer John Baird gives first public demonstration of television in London. And in 1992, Americans with Disabilities Act went into effect. Check out the Engineering Pathway’s resources on teaching and learning for persons with disabilities.
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Today in History – December 21, 1807 – Fourier introduces his series at the Paris Institute. Joseph Fourier’s memoir, On the Propagation of Heat in Solid Bodies, was read to the Paris Institute. It introduced the expansion of functions into trigonometric series which are now called Fourier series.

The Fourier series allows periodic functions to be represented as a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. The weights, or coefficients, of the components, arranged in order of increasing frequency, form a sequence (or function) called Fourier series. Fourier analysis provides a frequency domain representation of a time domain function. The mapping between the two functions is one-to-one, so the transform is reversible. A common visualization of this transformation is the audio equalizer, which is a dynamic representation of a time signal converted to the frequency domain. An audio spectrum of both time and frequency is shown below.

Preliminary work by Madhava, Nilakantha Somayaji, Jyesthadeva, Leonhard Euler, Jean le Rond d’Alembert, and Daniel Bernoulli would serve as the foundation for Fourier’s work. He applied his studies of trigonometric series to a solution of the partial differential heat equation to produce the series below:

Fourier’s initial series lacked the precision of a function, and Dirichlet and Riemann would later express the series as a formal integral.

Fourier series applications include electrical engineering, vibration analysis, acoustics, optics, signal and image processing, and data compression. Using the tools and techniques of spectroscopy, astronomers can deduce the chemical composition of a star by analyzing the frequency components, or spectrum, of the star’s emitted light. Similarly, engineers can optimize the design of a telecommunications system using information about the spectral components of the data signal that the system will carry.

For more information, see the Engineering Pathway‘s resources on Fourier and the Fourier series For related educational resources, visit the Electrical Engineering Education disciplinary community.

Today in History – December 13, 1928 – Today is Clip-on Tie Day. That’s right, on this day, 79 years ago, someone (and I couldn’t find out who) invented the clip-on tie. This fine fashion accessory often gets a bad wrap. People belittle it as the tie for people that don’t know how to tie a tie themselves.

If you are somehow unfamiliar with what a clip-on tie is, it is essentially a bow tie or four in hand tie which is permanently tied into its knot with a dimple just below the knot. Instead of looping around the neck, this tie is simply fixed to the front of the shirt collar with a metal clip. Though it doesn’t look as much like a real tie to fool everyone, and may accidentally come off with a too-hard tug, many people use clip-on ties every day.

The fact that a clip-on tie is likely to come off should it be tugged is actually a wonderful safety feature, especially for people such as police, paramedics, and engineers. Many of these occupations require personnel to use clip-on rather than full ties. Others might be mocked for wearing clip-ons because they don’t know how to tie a tie, or because they feel it is less restrictive, but the good old clip-on redeems itself by helping many wearers stay out of harms way. So here’s to that mysterious inventor of the clip-on tie. Harrah!

Meanwhile, to help make sure you’re never caught out not knowing what knot to tie, check out the Engineering Pathway’s resources on knot design and mathematics.