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SUMMARY:Camelia Karimianpour (University of Toronto\, Scarborough)
DTSTART:20210220T170000Z
DTEND:20210220T175000Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/1
DESCRIPTION:Title: “Dissection of Polygons”\nby Camelia Karimianpour (Uni
versity of Toronto\, Scarborough) as part of BIRS workshop: Geometry: Educ
ation\, Art\, and Research\n\n\nAbstract\nCertain contemporary problems in
geometry have their roots in mathematics covered in elementary school and
their further development can be understood gradually throughout high sch
ool and university mathematics. One such category of problems is related t
o the dissection of polygons. Geometric dissection of planar figures is in
troduced in elementary school when one computes the area of a polygon by c
utting it into pieces with disjoint interiors. The method works due to the
fact that the area is preserved under geometric dissection. Indeed\, the
famous Bolyai-Gerwin theorem states that any two polygons with the same ar
ea can be cut into polygons and rearranged to form the other. This stateme
nt 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 in
to tetrahedral pieces that rearrange into the other. The example was given
by Hilbert's student\, Dehn. \n \nUnderstanding the set-theo
retic dissection\, in which figures are cut into entirely disjoint pieces\
, requires higher mathematics and yields surprising results such as the Ba
nach-Tarski paradox that a solid ball B of any size can be finitely dissec
ted and rearranged to form two balls each congruent to B.\n\nIn this works
hop\, we will take an inquiry-based hands-on approach to investigate the p
roperties of geometric dissections of polygons\, and will prove the Bolyai
-Gerwin theorem only assuming high school algebra and geometry. We will al
so suggest inquiry-based activities to investigate other dissection relate
d problems. Our approach can be used by educators to develop extra curricu
lar materials and hopefully inspire artists to visualize some of these wel
l-known yet intriguing results. “\n \nAudience will need pa
per\, a ruler and a pair of scissors to fully participate in the workshop
activities.\n
LOCATION:https://stable.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:20260404T041857Z
UID:BIRS_21w2240/2
DESCRIPTION:Title: Mini-Course #1 (Part 1) with Ricardo “Kamikyodai” Hinojosa
: “Folding Sevens: The Power of Origami”\nby Sarah Brewer (The Ala
bama School of Mathematics and Science) as part of BIRS workshop: Geometry
: Education\, Art\, and Research\n\n\nAbstract\nThe sixth Huzita-Justin or
igami axiom\, first discovered by Italian mathematician Margherita Beloch\
, allows for geometric constructions not possible with a compass and strai
ghtedge. Some of the problems that stumped early geometers but are solvabl
e with this move include trisecting the angle\, doubling the cube\, solvin
g cubic equations\, and constructing regular heptagons. Utilizing origami\
, we will demonstrate how this so-called Beloch move is equivalent to find
ing the mutual tangent to two parabolas and unlock the mystery of a sevenf
old Islamic pattern.\n\nRecommended materials: \nPlain printer paper and p
encil/pen\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Greenwald (Appalachian State University)
DTSTART:20210220T200000Z
DTEND:20210220T203000Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/3
DESCRIPTION:Title: “Hands-on Geometry Explorations”\nby Sarah Greenwald (
Appalachian State University) as part of BIRS workshop: Geometry: Educatio
n\, Art\, and Research\n\n\nAbstract\nThe CBMS statement "Active Learning
in Post-Secondary Mathematics Education" highlights the importance of "cla
ssroom practices that engage students in activities." Hands-on geometry ca
n 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 gener
al education course\, to classes on geometry and differential geometry aim
ed at mathematics majors\, including future teachers. Some examples includ
e walking or driving an angle sum\, stringing the Pythagorean theorem\, an
d surfing a TNB frame. We use physical models and web-based GeoGebra IGS e
xplorations and p5.js experiences. Participants will have access to the wa
ys we use these in the classroom\, including related worksheets and the in
teractive activities themselves. We’ll also discuss student reactions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Plosker (Brandon University)
DTSTART:20210220T203000Z
DTEND:20210220T210000Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/4
DESCRIPTION:Title: “Indigenous Beadwork in a Mathematics Classroom”\nby S
arah Plosker (Brandon University) as part of BIRS workshop: Geometry: Educ
ation\, Art\, and Research\n\n\nAbstract\nIn this lecture\, I will discuss
the process of creating\, implementing\, and accessing the impact of an I
ndigenous beadwork assignment in a second-year undergraduate linear algebr
a course at my university. Emphasis is placed on the process behind the pr
oject\, including the motivation\, context\, and relationship building\, a
nd I will report our findings. This is joint work with Cathy Mattes.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State)
DTSTART:20210220T211500Z
DTEND:20210220T224500Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/5
DESCRIPTION:Title: Mini-Course #2 (Part 1) with Lara Kassab: “A Visual Introduc
tion to Geometric Data Analysis”\nby Henry Adams (Colorado State) as
part of BIRS workshop: Geometry: Education\, Art\, and Research\n\n\nAbst
ract\nWe give a visual introduction to several geometric techniques for an
alyzing data. These include both unsupervised learning (clustering\, dimen
sionality reduction\, topic modeling)\, and supervised learning (k-nearest
neighbors\, 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
visual and oral description without mathematical notation. The performanc
e of data analysis techniques will be illustrated on real-world image and
text datasets. Mini-course participants will be encouraged to develop thei
r own purely visual explanations\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/5/
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SUMMARY:Karl Schaffer (MoveSpeakSpin and also De Anza College)
DTSTART:20210221T170000Z
DTEND:20210221T175000Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/6
DESCRIPTION:Title: “Dancing with Circles”\nby Karl Schaffer (MoveSpeakSpi
n and also De Anza College) as part of BIRS workshop: Geometry: Education\
, Art\, and Research\n\n\nAbstract\nIn this session we will play with seve
ral surprising ways of exploring circles — and their properties — usin
g our bodies. This interactive session begins by looking at what happens w
hen we rotate our limbs in very simple movements\, and progresses to exami
ning swirling movements popular among contemporary dancers and choreograph
ers. We will explore whole-body circular activities easily done in a very
small space and will apply these actions to create movement sequences with
the ultimate mathematical prop — an ordinary sheet of paper. Then\, lea
rn how it all connects to the curious algebra of quaternions\, and see how
comprehending the embodiment of the quaternions helps us better understan
d both the mathematics and the relevant movement arts. No dance experience
necessary!\nMaterials needed:\n• Several sheets of ordinary printer pap
er\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
choreographer who co-directs the dance company MoveSpeakSpin\, and a math
professor at De Anza College.\n
LOCATION:https://stable.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:20260404T041857Z
UID:BIRS_21w2240/7
DESCRIPTION:Title: Mini-Course #1 (Part 2) with Ricardo “Kamikyodai” Hinojosa
: “Folding Sevens: The Power of Origami”\nby Sarah Brewer (The Ala
bama School of Mathematics and Science) as part of BIRS workshop: Geometry
: Education\, Art\, and Research\n\n\nAbstract\nThe sixth Huzita-Justin or
igami axiom\, first discovered by Italian mathematician Margherita Beloch\
, allows for geometric constructions not possible with a compass and strai
ghtedge. Some of the problems that stumped early geometers but are solvabl
e with this move include trisecting the angle\, doubling the cube\, solvin
g cubic equations\, and constructing regular heptagons. Utilizing origami\
, we will demonstrate how this so-called Beloch move is equivalent to find
ing the mutual tangent to two parabolas and unlock the mystery of a sevenf
old Islamic pattern.\n\nRecommended materials: \nPlain printer paper and p
encil/pen\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph O'Rourke (Smith College)
DTSTART:20210221T200000Z
DTEND:20210221T203000Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/8
DESCRIPTION:Title: "The Math Behind the Pop-up Spinner"\nby Joseph O'Rourke (
Smith College) as part of BIRS workshop: Geometry: Education\, Art\, and R
esearch\n\n\nAbstract\nPop-up books and cards have been around since the 1
8th century\, and recently have seen a surge in popularity through the ela
borate 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 func
tions turns out to depend on a geometric theorem concerning linkages prove
n in an undergraduate thesis. I will explain the connection and prove the
theorem.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Jungic (Simon Fraser University)
DTSTART:20210221T203000Z
DTEND:20210221T210000Z
DTSTAMP:20260404T041857Z
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:
Geometry: Education\, Art\, and Research\n\n\nAbstract\nIn this presentati
on\, I will give an overview of the Ubiratan D'Ambrosio's concept of ethno
mathematics and Elder Albert Marshal's concept of "two-eye seeing." I will
address some of the dynamics between these two concepts and illustrate th
em with two examples. The first example highlights geometry evident in a t
raditional Haida hat currently on display at the SFU Museum of Anthropolog
y. The second example draws from the work of contemporary Salish artist Dy
lan Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State)
DTSTART:20210221T211500Z
DTEND:20210221T224500Z
DTSTAMP:20260404T041857Z
UID:BIRS_21w2240/10
DESCRIPTION:Title: Mini-Course #2 (Part 2) with Lara Kassab: “A Visual Introdu
ction to Geometric Data Analysis”\nby Henry Adams (Colorado State) a
s part of BIRS workshop: Geometry: Education\, Art\, and Research\n\n\nAbs
tract\nWe give a visual introduction to several geometric techniques for a
nalyzing data. These include both unsupervised learning (clustering\, dime
nsionality reduction\, topic modeling)\, and supervised learning (k-neares
t neighbors\, support vector machines)\, though we don't expect you to kno
w what any of those words mean! The goal is to distill the methods down t
o visual and oral description without mathematical notation. The performan
ce of data analysis techniques will be illustrated on real-world image and
text datasets. Mini-course participants will be encouraged to develop the
ir own purely visual explanations.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w2240/10/
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