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BEGIN:VEVENT
SUMMARY:Camelia Karimianpour (University of Toronto\, Scarborough)
DTSTART:20210220T170000Z
DTEND:20210220T175000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/1
DESCRIPTION:Title: “Dissection of Polygons”\nby Camelia Karimianpour (University
of Toronto\, Scarborough) as part of BIRS workshop: Geometry: Education\,
Art\, and Research\n\n\nAbstract\nCertain contemporary problems in geomet
ry have their roots in mathematics covered in elementary school and their
further development can be understood gradually throughout high school and
university mathematics. One such category of problems is related to the d
issection of polygons. Geometric dissection of planar figures is introduce
d in elementary school when one computes the area of a polygon by cutting
it into pieces with disjoint interiors. The method works due to the fact t
hat the area is preserved under geometric dissection. Indeed\, the famous
Bolyai-Gerwin theorem states that any two polygons with the same area can
be cut into polygons and rearranged to form the other. This statement does
not hold in three dimensions however. Hilbert's third problem asks for an
example of two tetrahedra of the same volume that cannot be cut into tetr
ahedral pieces that rearrange into the other. The example was given by Hil
bert's student\, Dehn. \n \nUnderstanding the set-theoretic d
issection\, in which figures are cut into entirely disjoint pieces\, requi
res higher mathematics and yields surprising results such as the Banach-Ta
rski paradox that a solid ball B of any size can be finitely dissected and
rearranged to form two balls each congruent to B.\n\nIn this workshop\, w
e will take an inquiry-based hands-on approach to investigate the properti
es of geometric dissections of polygons\, and will prove the Bolyai-Gerwin
theorem only assuming high school algebra and geometry. We will also sugg
est inquiry-based activities to investigate other dissection related probl
ems. Our approach can be used by educators to develop extra curricular mat
erials and hopefully inspire artists to visualize some of these well-known
yet intriguing results. “\n \nAudience will need paper\, a
ruler and a pair of scissors to fully participate in the workshop activit
ies.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Brewer (The Alabama School of Mathematics and Science)
DTSTART:20210220T180000Z
DTEND:20210220T193000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/2
DESCRIPTION:Title: Mini-Course #1 (Part 1) with Ricardo “Kamikyodai” Hinojosa: “Fo
lding Sevens: The Power of Origami”\nby Sarah Brewer (The Alabama Sc
hool of Mathematics and Science) as part of BIRS workshop: Geometry: Educa
tion\, Art\, and Research\n\n\nAbstract\nThe sixth Huzita-Justin origami a
xiom\, first discovered by Italian mathematician Margherita Beloch\, allow
s for geometric constructions not possible with a compass and straightedge
. Some of the problems that stumped early geometers but are solvable with
this move include trisecting the angle\, doubling the cube\, solving cubic
equations\, and constructing regular heptagons. Utilizing origami\, we wi
ll demonstrate how this so-called Beloch move is equivalent to finding the
mutual tangent to two parabolas and unlock the mystery of a sevenfold Isl
amic pattern.\n\nRecommended materials: \nPlain printer paper and pencil/p
en\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Greenwald (Appalachian State University)
DTSTART:20210220T200000Z
DTEND:20210220T203000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/3
DESCRIPTION:Title: “Hands-on Geometry Explorations”\nby Sarah Greenwald (Appalac
hian State University) as part of BIRS workshop: Geometry: Education\, Art
\, and Research\n\n\nAbstract\nThe CBMS statement "Active Learning in Post
-Secondary Mathematics Education" highlights the importance of "classroom
practices that engage students in activities." Hands-on geometry can help
students make connections when kinematic and visual activities are linked
to visual processing and to mathematics. We'll share explorations we have
used in classes ranging from introduction to mathematics\, a general educ
ation course\, to classes on geometry and differential geometry aimed at m
athematics majors\, including future teachers. Some examples include walki
ng or driving an angle sum\, stringing the Pythagorean theorem\, and surfi
ng a TNB frame. We use physical models and web-based GeoGebra IGS explorat
ions and p5.js experiences. Participants will have access to the ways we u
se these in the classroom\, including related worksheets and the interacti
ve activities themselves. We’ll also discuss student reactions.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Plosker (Brandon University)
DTSTART:20210220T203000Z
DTEND:20210220T210000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/4
DESCRIPTION:Title: “Indigenous Beadwork in a Mathematics Classroom”\nby Sarah Pl
osker (Brandon University) as part of BIRS workshop: Geometry: Education\,
Art\, and Research\n\n\nAbstract\nIn this lecture\, I will discuss the pr
ocess of creating\, implementing\, and accessing the impact of an Indigeno
us beadwork assignment in a second-year undergraduate linear algebra cours
e at my university. Emphasis is placed on the process behind the project\,
including the motivation\, context\, and relationship building\, and I wi
ll report our findings. This is joint work with Cathy Mattes.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State)
DTSTART:20210220T211500Z
DTEND:20210220T224500Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/5
DESCRIPTION:Title: Mini-Course #2 (Part 1) with Lara Kassab: “A Visual Introduction to
Geometric Data Analysis”\nby Henry Adams (Colorado State) as part o
f BIRS workshop: Geometry: Education\, Art\, and Research\n\n\nAbstract\nW
e give a visual introduction to several geometric techniques for analyzing
data. These include both unsupervised learning (clustering\, dimensionali
ty reduction\, topic modeling)\, and supervised learning (k-nearest neighb
ors\, support vector machines)\, though we don't expect you to know what a
ny of those words mean! The goal is to distill the methods down to visual
and oral description without mathematical notation. The performance of da
ta analysis techniques will be illustrated on real-world image and text da
tasets. Mini-course participants will be encouraged to develop their own p
urely visual explanations\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/5/
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BEGIN:VEVENT
SUMMARY:Karl Schaffer (MoveSpeakSpin and also De Anza College)
DTSTART:20210221T170000Z
DTEND:20210221T175000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/6
DESCRIPTION:Title: “Dancing with Circles”\nby Karl Schaffer (MoveSpeakSpin and a
lso De Anza College) as part of BIRS workshop: Geometry: Education\, Art\,
and Research\n\n\nAbstract\nIn this session we will play with several sur
prising ways of exploring circles — and their properties — using our b
odies. This interactive session begins by looking at what happens when we
rotate our limbs in very simple movements\, and progresses to examining sw
irling movements popular among contemporary dancers and choreographers. We
will explore whole-body circular activities easily done in a very small s
pace and will apply these actions to create movement sequences with the ul
timate mathematical prop — an ordinary sheet of paper. Then\, learn how
it all connects to the curious algebra of quaternions\, and see how compre
hending the embodiment of the quaternions helps us better understand both
the mathematics and the relevant movement arts. No dance experience necess
ary!\nMaterials needed:\n• Several sheets of ordinary printer paper\n•
5 ft/ by 5 ft. area in which to move (non-carpeted area preferred)\n• A
belt and two ordinary (long) socks\nKarl Schaffer is a dancer and choreog
rapher who co-directs the dance company MoveSpeakSpin\, and a math profess
or at De Anza College.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Brewer (The Alabama School of Mathematics and Science)
DTSTART:20210221T180000Z
DTEND:20210221T193000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/7
DESCRIPTION:Title: Mini-Course #1 (Part 2) with Ricardo “Kamikyodai” Hinojosa: “Fo
lding Sevens: The Power of Origami”\nby Sarah Brewer (The Alabama Sc
hool of Mathematics and Science) as part of BIRS workshop: Geometry: Educa
tion\, Art\, and Research\n\n\nAbstract\nThe sixth Huzita-Justin origami a
xiom\, first discovered by Italian mathematician Margherita Beloch\, allow
s for geometric constructions not possible with a compass and straightedge
. Some of the problems that stumped early geometers but are solvable with
this move include trisecting the angle\, doubling the cube\, solving cubic
equations\, and constructing regular heptagons. Utilizing origami\, we wi
ll demonstrate how this so-called Beloch move is equivalent to finding the
mutual tangent to two parabolas and unlock the mystery of a sevenfold Isl
amic pattern.\n\nRecommended materials: \nPlain printer paper and pencil/p
en\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph O'Rourke (Smith College)
DTSTART:20210221T200000Z
DTEND:20210221T203000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/8
DESCRIPTION:Title: "The Math Behind the Pop-up Spinner"\nby Joseph O'Rourke (Smith C
ollege) as part of BIRS workshop: Geometry: Education\, Art\, and Research
\n\n\nAbstract\nPop-up books and cards have been around since the 18th cen
tury\, and recently have seen a surge in popularity through the elaborate
designs of pop-up masters like Robert Sabuda and Matthew Reinhart. But the
most stunning and elegant pop-up effect I have encountered is the Pop-Up
Spinner card invented by an anonymous Japanese student. How it functions t
urns out to depend on a geometric theorem concerning linkages proven in an
undergraduate thesis. I will explain the connection and prove the theorem
.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Jungic (Simon Fraser University)
DTSTART:20210221T203000Z
DTEND:20210221T210000Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/9
DESCRIPTION:Title: "Geometrical Shapes in Indigenous Art: Is This Mathematics?"\nby
Veselin Jungic (Simon Fraser University) as part of BIRS workshop: Geometr
y: Education\, Art\, and Research\n\n\nAbstract\nIn this presentation\, I
will give an overview of the Ubiratan D'Ambrosio's concept of ethnomathema
tics and Elder Albert Marshal's concept of "two-eye seeing." I will addres
s some of the dynamics between these two concepts and illustrate them with
two examples. The first example highlights geometry evident in a traditio
nal Haida hat currently on display at the SFU Museum of Anthropology. The
second example draws from the work of contemporary Salish artist Dylan Tho
mas.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State)
DTSTART:20210221T211500Z
DTEND:20210221T224500Z
DTSTAMP:20260422T185536Z
UID:BIRS_21w2240/10
DESCRIPTION:Title: Mini-Course #2 (Part 2) with Lara Kassab: “A Visual Introduction t
o Geometric Data Analysis”\nby Henry Adams (Colorado State) as part
of BIRS workshop: Geometry: Education\, Art\, and Research\n\n\nAbstract\n
We give a visual introduction to several geometric techniques for analyzin
g data. These include both unsupervised learning (clustering\, dimensional
ity reduction\, topic modeling)\, and supervised learning (k-nearest neigh
bors\, support vector machines)\, though we don't expect you to know what
any of those words mean! The goal is to distill the methods down to visua
l and oral description without mathematical notation. The performance of d
ata analysis techniques will be illustrated on real-world image and text d
atasets. Mini-course participants will be encouraged to develop their own
purely visual explanations.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w2240/10/
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