Dear friends,
As part of the work I direct at our Center we facilitate Global Learning
Network projects. One project we routinely facilitate is "Connecting
Math to Our Lives." I previously inquired about interest of XMCAers in
perhaps participating in some way in these. I did get positive
responses from Helena and Jay. I know that Helena, you became busy with
other priorities; and Jay I have been remiss in not getting back to you
sooner. I have been thinking about how best to involve folks without
having you be inundated with messages. Soon many of the participating
classes will be sharing back some varieties of data they've been
collecting around groceries and staple products, for some cross-country
comparisons. Jay, if you're still interested, and others, that may be a
time to review what the participants have done and offer some expert
advice on questions, issues and/or math concepts of import to their
deliberations. Let me know if that is of interest to anyone; feel free
to e-mail me directly.
In the meantime, below is a recent summary of some research carried out
by a class in Ghana who have sent this report on the local practice of
stilt walking. At the bottom of this message you'll find attached a
photo of a stilt walker. I don't mean to detract from the Sawyer
discussion or other threads. But perhaps this is of some interest to
XMCAers, who inevitably will find a way to weave it into current threads
and/or will accept this as a humble aside.
In Peace,
K.
-------- Original Message --------
Subject: Math Report (Stilt Walking) : 15-18/ENG -> ESP/Ghana
Date: Tue, 16 Apr 2002 10:02:41 -0700
Connecting Math to Our Lives: Class Introduction
(version en español abajo)
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GHANA: Local project report from educator William Asamoah Parbi and
students (ages 15-18) at Accra High School in Accra, Ghana.
E-mail: <aparbi@yahoo.com>
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Note from the coordinators: Please join us in congratulating William
and the students at Accra High School on preparing a carefully
researched and fascinating report on stilt walking in Ghana. What an
excellent example of mathematical problem solving and decision-making
in real life and of the sophisticated mathematical skills used by
people who have not traditionally been considered "mathematicians."
This report also adds to the important literature on Africa's
contributions to world culture and mathematics. Thank you, William!
We'll place this report along with the photo and data at the end (in
table-form) on our math web pages.
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William writes: "Attached is a photograph of a cultural display of my
country
men -- a man dressed in female costume standing on a Stilt. Stilt
walking is a traditional display as a form of entertainment in Ghana
by the people of Winneba. This is a continuation of what we sent to
you. If
there is any further information as to how we came by the
specification do not hesitate to get me informed. Hope to hear from
you soon."
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On the average, the length of the wood should be
280cm, diameter 6cm and 5cm respectively. This is so
because the wood has top face and bottom face; the top
face is tapered to the base hence the difference in
the diameter. The height of the person who stands on
the stilt is very important such that when the person
is tall he needs to use a shorter stilt. However, on
the average one needs to be about 1.66m tall. Again,
on the average the weight of the stilt walker should
be 66kg and that of the stilt 75kg.
The tensile strength of the stilt using the averages
should be 233.5 N/M2. This will however depend on the
weight of the person and cross sectional area of the
stilt chosen. The tensile strength is inversely
proportional to the cross sectional area so that the
smaller the cross sectional area the greater the
tensile strength. Again, the force that is expected
to exert on the stilt should be 66.0 N on the average.
It is also observed that at the point of equilibrium
the gravitational potential energy is a constant.
However, the kinetic energy is not constant for as
soon it becomes constant the person will fall. In
spite of these, the sum of the kinetic energy and the
gravitational force acting at a point in time should
be a constant.
There are various costumes used; what is in this
project is a male dressed like a woman. When the
stilt is too long, its centre of gravity reduces and
as such, care must be taken to avoid falling by
cutting the stilt to the required dimension. It is
alleged that some of them fall on slippery grounds as
such some of the stilt walkers are learning to balance
on slippery grounds. The following specifications can
be of use as others think of using plastic instead of
wood. In that case, the volume should be about 0.79m3
and weight about 75kg.
NAME
HEIGHT OF STILT WALKER
LENGTH OF STILT
WGT OF STILT
WGT. OF STILT WALKER DIAMETER TOP FACE/ BOTTOM FACE
AKWETE 162CM 280.4CM 74CM 65.5KG 6CM/5CM
MIKRONG 170CM 336.0CM 75CM 66.5KG 7CM/6CM
KOW ATTAH 165CM 270.0CM 74.5CM 65.4KG 6CM/5CM
KWESI TUNTUM 164CM 250.0CM 75.0CM 64.5KG 6CM/5CM
KOFI POH 150CM 264.0CM 74.6CM 65.5KG 5CM/4CM
AVERAGE 162.2CM 280.08CM74.6CM 65.48KG 6CM/5CM
William Parbi.
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GHANA: Informe sobre el proyecto local del maestro de matemática
William Asamoah
Parbi y los estudiantes (15-18 años) de la Escuela Secundaria Accra
en Accra, Ghana
Correo electronico: <aparbi@yahoo.com>
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Nota de los coordinadores: Les felicitamos a William y los
estudiantes de la escuela superior de Accra por una investigacion e
informe fascinante.
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William nos escribe: "Soy profesor de matematicas de la escuela
superior Accra en Ghana. Adjunto está una fotografía de un hombre
vestido de mujer de pie sobre zancos. Caminar en zancos es una forma
de entretenimiento tradicional de la gente de Winneba en Ghana.
Estamos interesados en investigar y decirles de las matemáticas
involucradas en esta tradición."
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En promedio, el largo de la madera debe ser 280cm, de diámetro 6cm y 5cm
respectivamente. Esto es así debido a que la madera tiene su parte de
arriba
y la de abajo; la de arriba está pegada a la base y a esto se debe la
diferencia en el diámetro. La altura de la persona sobre el zanco es muy
importante porque por ejemplo si la persona es alta tiene que usar un
zanco
más corto. A pesar de eso en promedio uno necesita medir 1.66m. Por el
otro
lado el promedio de peso del caminante sobre zancos debe ser 66kg y el
del
zanco 75kg.
La fuerza extensible del zanco utilizando los promedios debe ser 233.5
N/M2.
Esto aún así dependerá del peso de la persona y del área seccional
cruzado
del zanco escogido. La fuerza extensible es inversamente proporcional al
área seccional cruzado para que mientras más pequeño el área seccional
cruzado más grande la fuerza extensible. Nuevamente, la fuerza que se
espera
se ejerza sobre el zanco debe ser 66.0 N en promedio.
También se observa que en el punto de equilibrio la energía
gravitacional
potencial es constante.
A pesar de esto, la energía cinética no es constante porque en el
momento
que lo sea la persona se caerá. Aún así, la suma de la energía cinética
y la
fuerza gravitacional que actúa en cierto punto en el tiempo debe ser
constante.
Se usan varios tipos de disfraz y en este proyecto es un hombre vestido
de
mujer. Cuando el zanco es muy largo su centro de gravedad se reduce y
por
esto hay que tener cuidado para evitar caerse a través de cortar el
zanco de
acuerdo a la dimensión requerida. Se alega que algunos se caen en
terrenos
resbalosos y por esta razón muchos caminantes sobre zancos están
aprendiendo
a balancearse en terrenos resbalosos. Las siguientes especificaciones se
pueden usar si se piensa en usar plástico en vez de madera. En ese caso
el
volumen deberá ser aproximadamente 0.79m3 y el peso aproximadamente
75kg.
NOMBRE
ALTURA DEL CAMINANTE
LARGO DEL ZANCO
PESO DEL ZANCO
PESO DEL CAMINANTE DIÁMETRO DE ARRIBA/DE ABAJO
AKWETE 162CM 280.4CM 74CM 65.5KG 6CM/5CM
MIKRONG 170CM 336.0CM 75CM 66.5KG 7CM/6CM
KOW ATTAH 165CM 270.0CM 74.5CM 65.4KG 6CM/5CM
KWESI TUNTUM 164CM 250.0CM 75.0CM 64.5KG 6CM/5CM
KOFI POH 150CM 264.0CM 74.6CM 65.5KG 5CM/4CM
PROMEDIO 162.2CM 280.08CM 74.6CM 65.48KG 6CM/5CM
NB. Me informan por favor si la tabla no está muy clara para que yo
pueda
enviarla adjunta.
William Parbi.
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