The center node takes you to the work of Timothy Wei, professor and acting dean of Rensselaer’s School of Engineering, to see how he has solved Gray’s Paradox using his new state-of-the-art water flow diagnostic technology — Digital Particle Image Velocimetry DPIV — that measures the force a dolphin generates with its tail. Other nodes are about DPIV, how the US Navy trains dolphins (a retired Navy dolphin stars in the Rensselear video), general dolphin information (from the San Diego Zoo), and open courseware from Tufts University School of Veterinary Medicine on marine mammal medicine including care of dolphins, who are cetaceans.

The above image combines a map from the USGS Earthquake Hazards Program with a formula from a Connexions module by Sunil Kumar Singh that teaches forced oscillation. The map was captured as a screenshot from the USGS website 2 days after the Sichuan Earthquake began, and as the large squares on the map indicate, the aftershocks were continuing.

The Connexions module text accompanying the formula explains:

The resonance is an interesting feature of oscillation. This phenomenon attracts interest as it makes possible to achieve extra-ordinary result (material failure of large structure) with small force! Resonance also explains why earthquake causes differentiating result to different structures – most devastating where resonance occurs! The condition for maximum amplitude is obtained by differentiating amplitude function with respect to applied frequency as [the illustrated formula sets out.]

Thomas L. Pratt, who teaches research geophysicists at the University of Washington, provides a webpage that explains frequencies, periods, and resonance in which he includes this simple explanation: “Resonance is when motion at a given frequency is amplified by waves of that same frequency. For example, when a child is being pushed on a swing, the swinging is increased by a push being applied at the right time (at the correct frequency) during each swing.”

At Science Fair Central you can follow instructions for a simple experiment with 2 paper circles and a piece of cardboard to show why earthquakes shake some buildings more than others.

This learn node features a video called “The Arch Never Sleeps” in which professors explain the mechanics of the support arches provide for structures. One professor points out the limitations of laying a block of stone across two others. The professor whose foot is shown as he stands on an arch (that is not glued together) is demonstrating the strength of stone arches. The video is on a page from the Open University Mathematics and Statistics modeling problems open courseware.

If the concepts of arches and mechanical forces get curiosity strongly aroused, a popular online set of notes for the mathematics of mechanics can be found at the University of Nebraska-Lincoln. Included are algebra, geometry, trigonometry, analytical geometry, calculus and vectors � as each of them relates to mechanics. Or for more concrete contemplations of arches mathematics and more, there is a page titled Geometry of Bridge Construction by a Jesuit teacher of math. That site includes a quick explanation of the famed seven Bridges of Konigsberg problem and Euler’s solution that provides a key basis for understanding how the connectivity of the Internet makes it possible for learn nodes to form the webs from which ideas can emerge. Related in time and math concepts are the Medieval breakthroughs in math visible in mosaics from Islamic buildings.

More learn nodes at: learnodes.com