**
QUESTION 1**

**Date sent: Mon, 25 Sep 2000**

From: Matthias Kissel

Sehr geehrter Herr
von Glasersfeld,

könnten Sie mir
bitte wenigstens ein möglichst einfaches Beispiel geben für
den Beweis eines mathematischen Theorems unter Verwendung
imaginärer logischer
Werte? Ich suche schon lange danach,bisher leider vergeblich.

Danke!

° ° ° °
° ° ° ° ° ° ° ° ° ° ° °

Dear Mr. Kissel,

I answer your question in
English because I am sure you won't have
difficulties reading it.

When you say: "imaginary
logical values", I take it to mean "imaginary
numbers" - I don't know what else it should mean.

Let me state emphatically: I am
not a mathematician - but I have J.R.Newman's
"The World of Mathematics", a wonderful book that
has many times saved my
life.

In it, I quickly found an
answer to your question: The expression "(a
square + b square) multiplied by (c square plus d
square)" can transformed
into "(a+bi)(a-bi) (c+di)(c-bi), where "i" =
root of -1; if you then
carry out the indicated operations, you get the equation:
"(ac - bd)squared +
(ad + bc)squared". Which is considered "an
interesting and easily
verifiable theorem on numbers". This was easy enough for
me to understand, so it's
easy! Any mathematician will give you more sophisticated
examples.

Best wishes, Ernst von
Glasersfeld