- Cuchulainn
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This problem is flawed from the outset; it is not clearly defined.

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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I think we re still in the "try to convert photons emitted from pixels on the screen to triangles"-detection phase?

This problem is even more fundamental that e^5

This problem is even more fundamental that e^5

list1, give Cuch his account back!This problem is flawed from the outset; it is not clearly defined.

- Traden4Alpha
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Indeed!I think we re still in the "try to convert photons emitted from pixels on the screen to triangles"-detection phase?

This problem is even more fundamental that e^5

And given the curvature of space-time and quantization of materials, no triangles exist anywhere in the universe.

Indeed. But maybe it exists as a concept we all mostly agree on, in our consciousness?Indeed!I think we re still in the "try to convert photons emitted from pixels on the screen to triangles"-detection phase?

This problem is even more fundamental that e^5

And given the curvature of space-time and quantization of materials, no triangles exist anywhere in the universe.

This is all theory nonsense. Get practical and use a ruler!

Edit: Hmmm...different answers on PC and iPhone. I agree with Cuch, it's not properly defined.

Edit: Hmmm...different answers on PC and iPhone. I agree with Cuch, it's not properly defined.

What we have here is a brilliant capitalist examination question designed deliberately to encourage discussion and real in-depth learning, with VI Arnold, who was probably no fun at parties, going all po-faced and Russian and unable to think creatively.

He would clearly have been useless at what is now an important educational and creativity method known as the**Arctan School of Mathematics**.

He would clearly have been useless at what is now an important educational and creativity method known as the

- Traden4Alpha
**Posts:**23951**Joined:**

And now we have found another unstated constraint imposed by Russian thinking. Not only are some people imposing assumptions about numerical base and real numbers but they are also assuming the space is isotropic!This is all theory nonsense. Get practical and use a ruler!

Edit: Hmmm...different answers on PC and iPhone. I agree with Cuch, it's not properly defined.

Perhaps the hypotenuse is 10 inches and the perpendicular is 6 centimeters. Such a triangle would certainly "exist" in base-10 real number space.

- Cuchulainn
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You got sucked into one of Arnold's rants. If you know a little about him you would have known what I mean.list1, give Cuch his account back!This problem is flawed from the outset; it is not clearly defined.

http://www.datasimfinancial.com

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Cuchulainn
**Posts:**61185**Joined:****Location:**Amsterdam-
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You got sucked into one of Arnold's rants. If you know a little about him you would have known what I mean.list1, give Cuch his account back!This problem is flawed from the outset; it is not clearly defined.

Let's call it a draw

http://www.datasimfinancial.com

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Traden4Alpha
**Posts:**23951**Joined:**

Another unstated assumption is the required form of the answer. Is it a number (in some base and number system)? Can it be a formula? Can it be an essay?

- Cuchulainn
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In fairness, you were prepared to offer a 100-digit solution! I'm glad it's not a fixed-price project?Another unstated assumption is the required form of the answer. Is it a number (in some base and number system)? Can it be a formula? Can it be an essay?

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Cuchulainn
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Arnold's approach is a bit rigid ("geometry good, Bourbaki bad"). It is a long way from Polya's approach.What we have here is a brilliant capitalist examination question designed deliberately to encourage discussion and real in-depth learning, with VI Arnold, who was probably no fun at parties, going all po-faced and Russian and unable to think creatively.

He would clearly have been useless at what is now an important educational and creativity method known as theArctan School of Mathematics.

In real-life CAD you need algorithms that use both geometric and algebraic reasoning. Depends on which is more intuitive.

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Traden4Alpha
**Posts:**23951**Joined:**

30.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000In fairness, you were prepared to offer a 100-digit solution! I'm glad it's not a fixed-price project?Another unstated assumption is the required form of the answer. Is it a number (in some base and number system)? Can it be a formula? Can it be an essay?

- Cuchulainn
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The source is

*American school students had been coping successfully with this problem for over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why?*

12-years learn this. It's a language problem IMO which causes FUBAR. So in the diagram the line of length 10 _is_ the hypotenuse.

This is a good example for the annual science quiz. It will confuse everyone.

**The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.**

12-years learn this. It's a language problem IMO which causes FUBAR. So in the diagram the line of length 10 _is_ the hypotenuse.

This is a good example for the annual science quiz. It will confuse everyone.

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

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