Geometry

Millau Viaduct, France (2004) designed by Norman Foster

angles and polygons

• acute, right, and obtuse angles video
• how to use a protractor video
• angles tutorial
• create patterns
• estimating angles
• interactive quadrilaterals
• polygon definition
• interactive polygons
• make geometric solids and nets
• geoboard 1
• geoboard 2

transformations and tessellations

• translations, reflections, and rotations meaning of
• translations, reflections, and rotations tutorial #1
• translations, reflections, and rotations tutorial #2
• battleship against a computer
• battleship against a partner
• what is a line of symmetry?
• create lines of symmetry
• what is a tessellation?
• create tessellations
• tessellations in art ⇒ who is M.C. Escher?
• tessellations in architecture British Museum, London
• tessellations in architecture the World Trade Centre hub
• the oculus video

triangles and bridges

• interactive triangles
• types of triangles
• triangle tutorial
• bridges
• millau viaduct  foster + partners
• foster + partners  projects worldwide
• millau viaduct  video on design and construction
• the morandi bridge understanding why it failed
• above the clouds, the French glimpse the old grandeur

• Lord Norman Foster and Micheal Virlogeux designed the Millau Viaduct, the tallest bridge in the world. It gracefully spans the Tarn valley in Millau, France. The Millau Viaduct is a cable-stayed bridge with multiple cables, unlike the Morandi Bridge in Genoa, Italy which, lacking both robustness and redundant cables, catastrophically failed in the summer of 2018. The Morandi Bridge instead was supported by a single stay (cable) encased in concrete. This concrete encasement unfortunately prevented anyone from noticing any wear and tear in the cable that was cradled inside. The single cable design, combined with the internal rotting of the cable over time by the salty sea air, contributed to the unforgiving collapse. The sad twist to this tragedy is that the cables on one set of stays were entirely replaced in the 1990s. The bridge section that was supported by these cables remained in tact on that fateful day. Puzzlingly, the second set of cable stays were not replaced at all. In the end, it is this second set that failed on August 14th, 2018.  43 people lost their lives.

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