(12/28/97)
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MathMagic Cycle 26: Level 46 Regular
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A Bicycle in class???
A bet was made between the Betsy's Red Boxers team and Jorge's Teal
Sardines team regarding bicycles. Betsy's team says that the formula shown
is correct. Jorge's team,
number of teeth on the other hand, insists
wheel revolutions on wheel gear that the right hand side of
 =  the equation is upside down.
pedal revolutions number of teeth
on pedal gear To help them decide who is
right, your team needs to
bring a bike to class, along with masking tape and a measuring tape. You'll
need to use these items to first compare wheel revolutions and pedal revolu
tions (do you have enough measurements to predict a constant called GEAR
ADVANTAGE?)
You will want also to see relation between the number of teeth on the wheel
gear and the number of teeth in the pedal gear. The cross product of the
data accumulated will prove Betsy's or Jorge's team correct.
Are the above advantages somewhat more complicated on the multispeed bikes?
Perhaps you and your NTPs can challenge each other to set up an advantage
table for a fivespeed!
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MathMagic Cycle 26: Level 46 Advanced
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To determine the length of the hypotenuse of a fourth triangle you and
the team members are going to build some diamondshaped kites, except they
are going to be cockeyed. First join two dowels (perpendicular ribs) and
string three of the sides (Make sure they are not even  you must have
three different lengths of hypotenuses.) You are then going to record these
lengths and "measure" the fourth side. Repeat this
 process with three more lengths, until you have a
+ d total of four measurements (choose different sides
 every time). Now create a hypothesis that relates
+++ the sides and that seems to work with your data.
a  c
 Use a table like this one (data is given for 1st)

 ab  bc  cd  da  h1  h2  h3 
+ b +++++++
20" 15" 9"  __"   
++++++
      
++++++
      
++++++
      
++++++
(Hint: Cut the triangles before stringing & use squares and sums)
Did you arrive at a formula that perhaps can be applied to all
quadrilaterals?
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Good luck and best wishes for 1998
MrH