Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

Topic closed

**010595****Member**- Registered: 2016-08-16
- Posts: 2

never mind i did it...how do i delete posts?

restored from memory by BB

A company logo consists of a circle with an isosceles triangle inscribed inside so that the three vertices lie on the circumference. Prove that it is impossible for the area of the triangle to be exactly half that of the circle.

*Last edited by 010595 (2016-08-16 20:14:48)*

Offline

**Aeronaesis****Member**- Registered: 2016-07-18
- Posts: 7

Let

be the area of the outside segments.Assume that

This would mean that

Or that

Which is a contradiction, because the area of a circle doesn't equal base times height.

Offline

**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

hi 010595,

It can be proved if you are acquainted with maxima and minima in calculus. Please specify the topic on which you require solution..

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,273

hi 010595

Welcome to the forum.

There are several construction techniques that allow a triangle to be 'converted' into an equal area square.

It would be relatively easy to make that a square with twice the area of the triangle.

It has been shown to be impossible to construct a square equal in area to a circle,

https://en.wikipedia.org/wiki/Squaring_the_circle

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

Offline

**010595****Member**- Registered: 2016-08-16
- Posts: 2

Hi thickhead, the topic is based on trigonometry and circle geometry, no calculus...but not to worry I have solved it!!! Thankyou to all

Offline

**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

I too used trigonometry and used maxima.the area of the triangle comes out to be

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi 010595;

Please do not delete posts when other people have commented about them.

Does anyone remember this question so that I can restore it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,273

hi bobbym,

From memory it was

A company logo consists of a circle with an isosceles triangle inscribed inside so that the three vertices lie on the circumference. Prove that it is impossible for the area of the triangle to be exactly half that of the circle.

I have restored that above.

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

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi Bob;

Thanks. I am locking the thread to prevent further erasures.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,273

hi Aeronaesis

Which is a contradiction, because the area of a circle doesn't equal base times height.

True, but I don't think that 'proves' the impossibility. Say a rectangle was 6 π long and 6 wide; it would have an area of 36 π . This is the same as a circle with radius 6.

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

Offline

Pages: **1**

Topic closed