Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Circles #3

Prove that the line perpendicular to the tangent at its angle of contact passes through its center.

I did this through reductio ad absurdum. Is there any other way?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

Is there any other way?

I expect so, but proofs of this nature come from a set of axioms.  So what have you been given already?

eg.  How is a tangent to a circle defined?

LATER EDIT:

In book 3, proposition 18, of Euclid's Elements, he tackles this very problem.  You'll be pleased to know, he does it by contradiction! 

Bob

Last edited by Bob (2014-01-03 05:30:30)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Circles #3

Thank you

How is a tangent to a circle defined?

A line touching a circle at exactly one point

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #3

In book 3, proposition 18, of Euclid's Elements, he tackles this very problem.  You'll be pleased to know, he does it by contradiction! 

where can we find that book?

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

hi niharika

Well you could invent a time machine.  I believe there was a copy in the Great Library at Alexandria until it was burnt down.

If that proves too difficult then you can download it from

http://farside.ph.utexas.edu/euclid/elements.pdf

4.6Mb file so it will take a while and you'll need to use the 'find' command when you want to track down a proposition.  I search for the word 'tangent'.

Happy reading! 

Bob

Last edited by Bob (2014-01-03 21:14:30)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #3

thanks bob.

I will better download it soon rather than take some years to invent a time-machine and than having it.:)

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

hi Niharike,

You are not thinking 4 dimensionally.

(i) Go back in time and photograph the book.

(ii)  In a few years time invent the time machine.

(iii) Send the machine back to now so you can do step (i).

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #3

Wow! what a great idea.

You are really a genius.Well but I don't have time right now so will you be so kind to do those on behalf of me.

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

Thank you for those kind words. 

I've made a note in my diary to send the TM to you when I invent it.

Allowing 'time' for the time-lines to sort themselves out, that should happen any day soon.

If it doesn't, then we must conclude that I'll never invent a TM.

Maybe for the best.  There's some nasty paradoxes lurking about, just waiting to catch out the user of a TM. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Circles #3

But, could euclid speak englishh?

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

But, could euclid speak englishh?

This seems unlikely unless he had invented a TM.  Because English, as a language,  didn't exist in his time.  That's why the pdf is translated from the Greek.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: Circles #3

If he didn't speak english, then what's the use of inventing a TM and then going back to find a Greek book which I won't be able to even read.
Let's drop that idea and use that pdf (which is a much better option) and be happy.

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friendship is tan 90°.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Circles #3

Thank you for those kind words. 

I've made a note in my diary to send the TM to you when I invent it.

Allowing 'time' for the time-lines to sort themselves out, that should happen any day soon.

If it doesn't, then we must conclude that I'll never invent a TM.

Maybe for the best.  There's some nasty paradoxes lurking about, just waiting to catch out the user of a TM. 

Bob

Another way would be being in a big danger. Then the Doctor might pick up on your fear using his psychic paper.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

Good idea.  I'll climb inside a dustbin waving a sink plunger and screaming 'exterminate' in a funny voice.  Maybe that'll attract him. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Circles #3

Or you can just get inside your wardrobe in hopes of being attacked by oversized dolls.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Circles #3

That happens to me all the time. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob