[PDF] GEOMETRY TRAIL - Thinking 3D





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[PDF] GEOMETRY TRAIL - Thinking 3D

If you could only use one of these to study advanced geometry, which would you find most useful? The categorisation of page after page of polyhedra in

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[PDF] GEOMETRY TRAIL - Thinking 3D

GEOMETRY TRAIL If you could only use one of these to study advanced geometry, which would you The categorisation of page after page of polyhedra in

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[PDF] GEOMETRY TRAIL - Thinking 3D 5468_6T3D_Geometry_Trail.pdf Luca Pacioli was one of the most famous maths teachers of the Renaissance.

In the picture on the wall, which objects

is he using to teach?

Look around the exhibition to find polyhedra

represented in different ways:

GEOMETRY TRAIL

Poly (many) + gonos (angled) = polygon

Poly (many) + hedra (seat/base/face) = polyhedron Ge (earth, land) + -metria (a measuring of) = geometry Look

Think

Write

hand-drawn diagrams printed images with solid sides printed images with only edges shown nets showing the whole shape nH[SORGHGo paper, wooden and plastic models If you could only use one of these to study advanced geometry, which would you find most useful? Two books on maths published by Luca Pacioli are in this exhibition. Compare these two books. Who illustrated the later one, and what made the diagrams more effective than the illustrations for the first book? 6

3MŃLROLoV VHŃRQG NRRN ŃRQPMLQV POH ILUVP HYHU SULQPHG

illustration of the elevated icosidodecahedron.

Nearby, find another way of illustrating 3D

geometry which was a world first. The icosidodecahedron has 20 triangular faces and

12 pentagonal faces. The elevated icosidodecahedron

is made by creating a pyramid of equilateral triangles on each face. How many triangles would you need to do this? ffff 5 Instead of being hand-written, the books in this display case were printed on printing

presses, with woodcut illustrations. Pacioli wrote in Italian, and Dürer wrote in German (although

the Latin translation is on display here.) What difference would the new technology of the printing press and the choice of language have made for Renaissance learning?

Name: fffffffffffff

Johann Kepler used the astronomical data gathered by astronomer Tycho Brahe to create his three laws of

SOMQHPMU\ PRPLRQB .HSOHUoV POHRULHV NXLOP RQ POH

sun-centred model of Copernicus by defining the SOMQHPVo HOOLSPLŃMO RUNLPVB HQ PXUQ HVMMŃ 1HRPRQ XVHG .HSOHUoV LGHMV PR ŃRPH XS RLPO OLV OMR RI universal gravitation.

Why do you think Kepler also created

this strange diagram, where the orbits of the six known planets are overlaid with the five Platonic solids? (XŃOLGoV Elements is the most influential textbook in the world. Written around 2,300 years ago, it collects the mathematical wisdom of the ancient Greeks, applying mathematical logic to the three-dimensional world by defining 2D and 3D shapes. The book survived at first by being copied by hand.

Find a Greek version made in 888CE by a scribe

called Stephanus. He illustrated the text with simple pen and ink diagrams. )LQG POH ILUVP (QJOLVO PUMQVOMPLRQ RI (XŃOLGoV

Elements . Published in 1570, and printed rather

than hand-RULPPHQ POH PUMQVOMPLRQ OHP SHRSOH ROR GLGQoP speak Greek study this key mathematical text. What else did the author do to make his illustrations clearer, and help students understand geometry? fffffffffffffffffffffffffffffBB 1 14 18 The categorisation of page after page of polyhedra in

0M[ %U×ŃNQHUoV RRUN PLJOP VHHP SRLQPOHVV PR VRPHB 30

But why do you think humans have been fascinated by geometry for thousands of years? Look around the exhibition and list some reasons why people might study geometry. ...............................................................................................

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All images Ξ Bodleian Libraries, Uniǀersity of Odžford, edžcept detail of

Luca Pacioli with a student

, 1495, reproduced with permission of the Museo di Capodimonte, Naples.

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