Just ordered large pizza and asked that it be cut into 10 equal parts
as in traditional cartwhheel configuration, but lady at counter said
she cant work out how to do it.  Is there a simple way that has some
geometric methodology to it, or is it a matter of just practice makes
perfect as in just memorising where the cuts should roughly be.

 Johnfrommelbourne

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Clarification of Question by johnfrommelbourne-ga on 24 Jan 2003 05:29 PST

Not necessarily a technically true geometric means perhaps but just a
simple way of getting the result required would do fine. I mean there
just may be a simple little trick to it that uses some simple
reference poiint that makles it easy. for instance to cut pizza into
twelve  just requires a  clock face sequence of lines I now see just
in this last half hour after toying with issue.

Well John,

You had me fooled. You’ve taken a complex Euclidian geometric puzzle
and disguised it as a simple Pizza question. Nice work!

The answer is simple – Just take this drawing and a compass or a
protractor to your pizza lady next time, and she’ll be the first in
her neighborhood to be able to be able to divide a circle into 10
equal parts!

http://www.i-am-a-i.org/read-only/illustrations/Mandala__05(easy).jpg

The template is based on Euclid’s pentagram geometric construction. It
illustrates the golden section which is unique in that it can divide a
circle into ten equal parts.

Ok, so I jest. 

The fact is, the circle does not divide easily or naturally into ten
equal parts but there are a couple of ways an adroit pizza lady (or
you) could eyeball it and get a close-enough division.

FIRST WAY –

Roughly mark out a pentagon that spans the pizza
Cut from the center of the pizza to each corner of the pentagon
Cut each of those 5 slices in half. 

EUCLIDS CONSTRUCTION OF THE EXTREME AND MEAN RATIO
http://splorg.org/~b/works/golden/


SECOND WAY –

Divide the pizza into quarters.

Divide each quarter into 5 fairly equal slices. Make the slice
continuous from one edge of the pizza to the other, so you are
effectively cutting 2 opposing quarters with the same draw of the
knife.

Give everyone 2 slices - to equalize the portions, give each person
two that oppose each other on the circle, not adjacent slices.


Or, you could just invite two more friends to the pizza party.  :-)

Hope this has helped –

K~

Search terms:

“circle into ten”  -recipe -recipes
“circle into 10”
“pizza into ten”


*note: it surprised me how many recipes instructed – “slice the
pie/cake/ into ten wedges” as if that’s an easy thing to do. Wonder
how many of those cooks keep their geometry books handy....

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Clarification of Answer by knowledge_seeker-ga on 24 Jan 2003 05:58 PST

Hey John,

For this link --

EUCLIDS CONSTRUCTION OF THE EXTREME AND MEAN RATIO 
http://splorg.org/~b/works/golden/ 

Do 3 PgDn's to get to the drawing I meant for you to see. :-)

-K~

Yes very well done Knowledge-seeker and made entertaining reading as
well. And yes you are right I really am a master mathemetician
specialising in geometric puzzles just trying to test the skills of GA
researchers, incognito

The following pizza incident is attributed to Yogi Berra, but it may be apocryphal:

When asked if he wanted his pizza cut into four slices or eight, Yogi replied:

“Better make it four.  I don’t think I can eat eight.”

Hold the anchovies – ddelphi.

Use a protractor, and cut 36 degree sized slices...  >:-}

-- Anduril-ga

Here's an easy way to cut pizza, cake, pie, etc. into 10 (roughly)
even slices. It sounds more complictated than it is - try it using an
empty plate to see what I mean.
1. Starting from the top of the pizza, cut down to the bottom to cut
it in half.
2. Starting at about 10:00 (picturing a clock face), slice completely
across to the opposite side, leaving two large "quarters" and two
small "quarters".
3. Cut once through the smaller "quarters", leaving four pieces.
4. Cut twice through the larger "quarters", giving the other six
pieces.

Hope this helps.
alex_p

Ok Alex, will try that as I have just arrived at work and just opened
up emails.
 You must have been scanninmg old posts I assume and justa come across
this one yes?

 John From melbourne

Yup. I'm just back from holidays and wanted to see if there was
anything interesting in GA (like your question John).