(12/28/97)

(Reminder to *REGISTERED* teams: You can now work with Net Team Partners
(NTPs) that are not registered, just subscribed to the "mathmagic-4-6-
open" list. Feel free to advertise your team name, location and e-mail,
along with the geographical location of the desired partner. To do so, 
just send an e-mail to mathmagic-4-6@mathforum.org. PLEASE remember 
this only works if you have paid and been included in one of the WELCOMES 
regularly posted.)


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MathMagic Cycle 26: Level 4-6 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 multi-speed bikes?
Perhaps you and your NTPs can challenge each other to set up an advantage
table for a five-speed!

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MathMagic Cycle 26: Level 4-6 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 diamond-shaped 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