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#1 2013-03-16 10:58:36

n872yt3r
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Registered: 2013-01-21
Posts: 392

Pi Day Challenge And Happy Pi Day

There is an awesome challenge online. Since yesterday was pi day (March 14) they have something really cool.
www.pidaychallenge.com
3.14159265358979... Ok.
It's a series of levels where you have to answer lots of math questions.
Here are some of the questions below:
1. Name the first 5 decimal digits of pi.


3. (This is a trick question) What does the license plate say?

6A. The ___________ Theorem states that for any right triangle, the sum of the lengths equals the square of the length of the hypotenuse.

6B.
What is x?

9. What are the roots of the function

11. What is Archimedes' ratio approximation of pi?

I'm completely stuck on #23:
You run downwards at a speed of 3 steps per second.
It takes you 180 steps to get to the bottom.
You walk upwards at a speed of 1 step per second.
It takes you 20 steps to get to the top.
How many steps do you need if the escalator stands still?

Last edited by n872yt3r (2013-03-16 23:02:19)


- n872yt3r
Math Is Fun Rocks! smile
By the power of the exponent, I square and cube you! cool

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#2 2013-03-16 16:11:48

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Pi Day Challenge And Happy Pi Day

Happy Pi Day and Thanks for the link

Is that the full statement of the problem?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#3 2013-03-16 22:45:51

n872yt3r
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Registered: 2013-01-21
Posts: 392

Re: Pi Day Challenge And Happy Pi Day

It's all they tell me. There's another incomplete question. You have to find the area of the blue shaded area of a triangle with 10 equally tangent circles inside, but you can see the side or the radius.


- n872yt3r
Math Is Fun Rocks! smile
By the power of the exponent, I square and cube you! cool

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#4 2013-03-17 00:04:47

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
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Re: Pi Day Challenge And Happy Pi Day

I am also struck at that equilateral hmm


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#5 2013-03-21 02:54:22

digits
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Registered: 2013-01-02
Posts: 6

Re: Pi Day Challenge And Happy Pi Day

Oh!
I forgot to wish everybody Happy Pi Day on March 14th!
Hope it was good for you all.
Cheers! digits


Bring me my Bow of burning Gold!
Bring me my Arrows of Desire!

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#6 2013-03-29 22:41:28

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
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Re: Pi Day Challenge And Happy Pi Day

Answer: 60 steps


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#7 2013-03-29 23:14:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

Hi;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#8 2013-03-29 23:16:14

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
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Re: Pi Day Challenge And Happy Pi Day

My father helped me


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#9 2013-03-29 23:28:33

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

Looks like I needed the help...


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#10 2013-03-30 01:50:43

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

Re: Pi Day Challenge And Happy Pi Day

Thanks guys now I'm on 26; it's not an actual problem but a visual logic puzzle.


- n872yt3r
Math Is Fun Rocks! smile
By the power of the exponent, I square and cube you! cool

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#11 2013-11-18 15:38:37

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
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Re: Pi Day Challenge And Happy Pi Day

Hi bobbym,

Can you walk me out through problem 22


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#12 2013-11-18 22:14:00

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

Problem 22? I do not know it?!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#13 2013-11-19 00:33:42

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

There are 10 circles each of radius 3 cm stacked like this:
   *
  * *
* * *
* * * *

Then they are being inscribed by a triangle. Something like this, but more tightly, I mean perfectly inscribing:
      ^
   /   *  \
  /  * *   \
/  * * *   \
/   * * * *  \
________

What is the area of that triangle?

The person below enjoyed that ASCII art


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#14 2013-11-19 03:54:30

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

How close must the answer be and what type of answer?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2013-11-19 04:04:07

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

That is not important. I only want to know how it is done


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#16 2013-11-19 04:09:40

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

An analytical solution is different than a numerical one. Do you need a closed form?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#17 2013-11-19 04:11:46

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

What is a closed form? I would say an analytical one because the radii of the circle may be different


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#18 2013-11-19 04:18:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

An expression is said to be a closed-form expression if it can be expressed in terms of a finite number of elementary expressions.

is in closed form

is not.

Both represent numbers but the integral is not an elementary function.

Perhaps a better question is, do you want an exact answer?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2013-11-19 04:27:31

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

no, I want to know how the question can be attacked


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#20 2013-11-19 04:33:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

Numerically will yield an answer quickly. Then the only question is one of accuracy.

For instance the triangles area is approximately 350 cm.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#21 2013-11-19 04:35:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

Numerically will yield an answer quickly. Then the only question is one of accuracy.

I do not want the answer badly. I've already cracked the answer by intellignet brute-force


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#22 2013-11-19 04:40:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

Then I am interested in what you did.

I would do it in one of two ways. Use geogebra to make a very fine diagram and extrapolate to the answer by making several ansatzes.

I would place the circles one using simultaneous equations and then figure the triangle that would enclose them. It will require M.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#23 2013-11-19 04:43:17

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

That puzzle had an option, either you can ask for the length of the sides of the triangles or the radii of the circles.
Unfortunately, each time I refreshed the page, the problem was regenerated with new values


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#24 2013-11-19 04:53:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Pi Day Challenge And Happy Pi Day

I also would first investigate all the literature.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#25 2013-11-19 05:29:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,112
Website

Re: Pi Day Challenge And Happy Pi Day

Using what kind of a search algorithm?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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