1) Pizza Areas
From: "Walter Whiteley"
Subject: Re: Real Life Uses of the Pythagorean Theorem
To: uc@mathforum.org (Roger Schmitt)
Date: Fri, 24 Jan 1997 15:13:56 -0500 (EST)
Roger
Here is a cute application:
Consider two medium pizza's and one large pizza. Without
calculating any dimensions (as number) determine the relationship
between the sum of the areas of the medium pizza's
and the area of the large pizza.
Solution:
Make a triangle using two sides AB, BC as the diameters of the medium
pizza's and the 'hypotenuse' AC as the diameter of the large pizza.
If the angle ABC is less than 90 degrees, the large pizza has less area;
= 90 degrees the large pizza has equal area;
more than 90 degrees, the large pizza has more area.
Walter Whiteley
York University
2) Add up the Squares. Origin of Distance Formula.
Date: Sat, 25 Jan 1997 09:35:30 -0700
From: Diane Thompson
To: Roger Schmitt
Subject: Learning the Pythagorean Theorem
>I would like help explaining to my students the use of the "Pythagorean
>Theorem". This proficiency has also appeared on the EWT in a few different
>forms, such as finding the diagonal of a square or a rectangle.
snip
Several years ago I approached this by having students draw some
right triangle on graph paper, construct the "squares" on the legs and
hypotenuse, and then reassemble the smaller squares to show that they had
the same dimensions as the square whose side was the length of the
hypotenuse ... we used that ugly graph paper that is typically in American
schools ... the students disproved the theory! It seems that the graph
paper is poorly made and most students came out with 2 and a fraction extra
squares!
But, of course, these construction exercises for the Theorem are somewhat
useful in helping students really understand.
I have found the most useful technique is to constantly malign (verbally)
the "Distance Formula". I never use it without heaping scorn on memorizing
it etc ... and I go through this little tirade about how it is just the
right triangle and the sides are figured out this way ... I draw it as I
talk and find the lengths of the sides that way, compute the value I'm
looking for, and end by drawing them back to the form of the Distance
Formula. Lots and lots of times, then, they are hearing about the
Pythagorean Theorem and its use as a TOOL
Diane Thompson
3) House TV Show Videos
Date: Fri, 24 Jan 1997 15:39:37 -0800 (PST)
From: "Nancy J. Christolear"
Subject: Real Life Math Examples
To: uc@mathforum.org
Hi,
If you can get copies of video tapes from Hometime, Yankee Workshop or This
Old House on PBS, you will find that on episodes where they install roof
rafters or stair risers or even some of the furniture, there is quite a bit
of angle calculation.
Nancy
4) Carpenters and Construction
Date: Thu, 30 Jan 1997 03:32:05 +0100
From: Jeff Winger n9141816@cc.wwu.edu
To: uc@mathforum.org
Subject: pythagorean theorem
Hello, my name is jeff winger. I'm an elementary education student at
western washington university in Bellingham Wa. I was browsing and saw
your posting. I haven't even taught one math lesson yet but I do have a
good idea for you. Carpenters, as you can imagine use a lot of geometry,
and here is one good example of practical use of the pythag. theorem. To
determine quickly whether two walls or 2X4s or what have you are joined
at an an angle of exactly of 90 degrees, they often use their tape
measure and take a "three,four, five". From the inside of the corner
they measure out three feet (36in) and mark it. Then, they measure down
the other board or wall four feet (48in) and mark the spot. Then you
measure from the first mark to the second and you should measure out
exactlly five feet (60in.) if your wall is indeed at a 90 degree angle
and if not you make your adjustments! It is a simple way to preform the
function of the theory without time consuming calculations on the job.
Please let me know if this serves your purpose.
5) Real Math Field Trip
Date: Fri, 31 Jan 1997 00:57:36 -0800
From: Wes Treen wtreen@junction.net
To: Roger Schmitt
Subject: Re: Real Life Uses of the Pythagorean Theorem
Hi Roger
I know you posted this a week ago ,but ...
The greatest inspiration I can think of to get kids to try to
grasp Maths' fundamentals, would be to arrange a field trip through
various occupations in which math is a definate necessity.
ie. Machine shops , Autocad drafting{architects},Pipe fitters and
boiler makers,carpentry and jointery,mill-wrights,sheet metal and
fabrication, to name a few. Encourage the students to ask the employees
in which way they require math in their everyday chores and tasks.
' Hope this idea helps
Regards
Wes Treen.
Machinist,Power Engineer, Fluid-power Tech.
6) Angle Braces
From: Kim_B._Wallmark@pds.k12.nj.us (Kim B. Wallmark)
To: uc@mathforum.org
Subject: Re: Real Life Uses of the Pythagorean Theorem
Date: 06 Feb 1997 20:50:08 GMT
Organization: Princeton Day School
Triangular bracing is often used to stabilize buildings and tables. Do you
have a shop class or an architecture class at your school? Maybe that
teacher could give you some specific examples.
--Kim