# Math Is Fun Forum

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

You are not logged in.

## #2 This is Cool » Mathematics of quena flute » 2020-09-24 00:23:52

George,Y
Replies: 1

These guys are truly genius!

## #3 Re: This is Cool » Mathematics of Rotary Engine » 2020-09-04 00:11:01

It is based on cycloid, traditional technology used on watches.

## #4 Re: This is Cool » Mathematics of Rotary Engine » 2020-09-03 14:33:40

Thanks Bob!

bob bundy wrote:

hi George,

Bob

The old rotary engine is beautiful in theory, but  has many engineering flaws that make it vunerable

Why wan-kel rotary has no future

Hence there are many geniuses inventing new form of rotaries, for example:

a new rotary engine vs wan-kel

The rotaries fits in the chamber quite neat, huh?

How are they fit into the chambers and how to determin the axis?

These are very interesting math questions.

## #5 Re: This is Cool » Mathematics of Rotary Engine » 2020-09-02 18:08:50

w-a-n-k-e-l
Why this five letters are censored in this forum?
He is the enemy of the moderator?

## #6 Re: This is Cool » Mathematics of Rotary Engine » 2020-09-02 18:02:44

What is happening? The end of the link is supposed to be math instead of math

Why automatically it is changed?

## #7 This is Cool » Mathematics of Rotary Engine » 2020-09-02 17:59:57

George,Y
Replies: 5

Rotary Engine, despite the difficulties to make it, Mazda still use it for cars and vehicles.

The most fascinating advantage is that this type of engines transfers the power of explosion of fuel directly to rotary motion of axis.

math's rotary motion has stand with time, however, there are many other inventions to challenge this type.

Let's ignore the physics and engineering part, by just focusing on the rotary part and the part surrounds it.

Can you explain it by Mathematics?

## #8 Re: Help Me ! » P(aub) =p(a) +p(b) -p(a&b) » 2020-02-01 01:36:11

The logical definition of A&B is that both of them are true.

Thus from a logical point of view, !A and A cannot be true simultaneously. This is by definition of logic.

also !A+A = ALL

B = (!A U A)&B =  ( !A&B )U (A&B)

The first equal sign is self-explanatory, here is the rational for the second:

If a case belongs to !A&B, it must belong to (!A U A)&B since !A U A contains !A
same for A&B
Therefore the left contains the right

you can then prove the right contains the left from a similar logic.

Therefore
B contains A&B.

## #9 Re: Help Me ! » Hard exercise with positive terms » 2019-12-12 19:24:18

I suggest you first thing first, simplify the fraction

i.e. k^(1/3)/k^2 = k^(-5/3)

Then you can try add them together?

## #10 Re: This is Cool » The mathematics of mosques » 2019-12-12 00:57:35

I feel like Islam is a reborn of Zoroastrianism.
the shape of a Mosque top is the shape of a flame.

## #11 Re: Help Me ! » Applying the cauchy criterion when the series are not convergent » 2019-12-05 19:22:00

(n+1)/(3n+2)

> (n+1)/(3n+3) = 1/3

(m-n) * 1/3 does not satisfy Cauchy Critirion

thus ∑1/3 is not convergent (even without using Cauchy Critirion)

How can  ∑(n+1)/(3n+2) , a larger one, converge?

## #12 Re: Help Me ! » [ASK] Prove » 2019-11-29 20:41:48

https://www.mathsisfun.com/algebra/trigonometric-identities.html

## #13 Re: Help Me ! » College Struggles » 2019-11-28 00:03:36

My pleasure

math9maniac wrote:

Hello George,Y

I appreciate your input and words of advice. You and bob bundy have helped and motivated to own my education and stand up for myself. I only wish I didn't expect too much, and that from beginning, someone would have told me that college is so much different from high school. There are so much I wish I had known earlier.

Regards

## #14 Re: Help Me ! » College Struggles » 2019-11-25 23:33:40

Hello math9maniac,

Your situation seems somewhat alike with my experienc in a graduate school, where math professor is not a very good conveyer of the subject.

However, my experience was that few assignment is better than many but not responsible assignment. I mean the assignment could be totally outside of teaching and tedious, just to make you busy and make the class "sound". I am glad that the professor at least does not mean to rob your time. Therefore you do have a choice to study alone.

About tutorial, tutor or textbook. I believe the most apprehensible for now is most valuable. I self studied stochastic calculus for several times, each time getting more experienced and advanced with the subject before becoming an expert in this field. I regret not begining from the basics and understandable when I was in college. I just finished every assignment every week(some took 2 days) and got good GPA though not quite got the subject.

About assignment. I believe the understanding of the topic, the understanding about the proofs are more important than simply "dog training" application like assignment.

Briefly, find a good tutor, find some good books starting from the basic and learn by yourself. You will not be confused.

## #15 Re: Help Me ! » Calculating the probability of coin being biased » 2019-11-19 23:39:02

It is a classical p-value test
But I would argue that this test cannot judge probability.

I suggest you read Bayesian statistics. I guess this problem is a false one.

## #16 Re: Help Me ! » The Last Few Terms in an Infinite Series » 2019-11-19 23:34:45

Old post 0.999... = 1?
http://www.mathisfunforum.com/viewtopic.php?id=658

## #17 Re: Help Me ! » Statistics and Economics » 2019-11-19 23:30:14

Hello, I think you are asking the subject of "Econometrics"

You see, probability deals with theoretical models, where as statistics faces real world difficulties.

You can view statistics as "applied probability". But as facing real world data, the former probabilitists found there are much more details they have to solve than good and old probabilities and they have been improving the original theory again and again.

Therefore on the practical side, statistics have evolved into Econometrics after scores of years of struggle.
If pure probability was good old Newton physics, statistics could be termed as mechanics.

## #18 Dark Discussions at Cafe Infinity » His Dark Materials - Wizard against Christianity? » 2019-11-18 01:17:17

George,Y
Replies: 0

I have watched a movie called "Golden Compass"
It claims christianity castrates children. And to save the children, they must fight against christian priests.

Is it some propaganda by Wizards or Alchemists?
Anyone more familiar with the story than me?

Also Harry Potter could be seen as a successful propaganda by Wizards.

As far as I know, there are at least three schools different religions in Europe:
Wizard, Alchemists against Christianity

## #19 Re: Help Me ! » Explanation for Multiplying/Dividing in Equations/Inequalities » 2019-11-15 15:51:42

A=4x+(3/4)-1
B=5+20
A = B
thus
kA = kB
A/k = N/k as long as k<>0
A+k = B+k

## #20 Re: This is Cool » Cross Redundency Reliability Probability » 2019-11-13 01:57:20

s(p)/c(p) -> 2 as p->0

## #21 Re: Help Me ! » Conversion of recurring decimal to fraction algebraically » 2019-11-13 01:40:42

bob bundy wrote:

hi George,

That's as good a reason as any I suppose.  At school, geometry was my best topic and I rather like that gif as it has some interesting properties as you say.  From what I can remember I used some static geometry software to make the diagram and then animated it in flash.  That's about the extent of my flash programming though.  Once I made it I decided to stick with it.

I felt strange about it. A famous Chinese mathematician Hua Luogeng preached 0.618 rule, orginated by Jack Kiefer, to substitute bisection method.
Do you know why it improves efficiency? Or does it improve efficiency at finding roots?

## #22 Re: Help Me ! » Conversion of recurring decimal to fraction algebraically » 2019-11-12 23:00:02

bob bundy wrote:

hi George,

Yes it does in a way.

Bob

Hi Bob, I think both views have their rational.

By the way, you seem to be fond of pentagons. Is it because it contains the golden ratio phi = (√5 -1) /2 ?

## #23 This is Cool » Cross Redundency Reliability Probability » 2019-11-12 22:55:16

George,Y
Replies: 1

I designed a server sytem and its backup plan.

To simplify, there are a pair of server programs  each using one hard server.
And redundancy makes a pair of them.

This is the original plan:

A1 A2
|    |
B1 B2

But since A's are equivalent and B's are equivalent I come up this:

A1 A2
|  X  |
B1 B2

A1-B2 and A2-B1 also works.

Now comes the fun part: reliability
Suppose the manufacturer can only guarantee the failure rate of each hard server as little as p

How is the overall A-B server system failure rate?

For the straight pair, the failure situation is not a single pair could work (They both fail)
[1-(1-p)(1-p)]^2 = [p(2-p)]^2

For the cross enhanced, the success situation is both A's and B's have at least one functional:
[1-pp]^2

So the survival rate of the straight is S(p) = 1 - [p(2-p)]^2  ; failure rate s(p) = [p(2-p)]^2
the survival rate of cross enhanced is C(p) = [1-pp]^2  ; failure rate c(p) = 1 - (1-pp)^2

Usually, s(p) = 2c(p)
Or the cross pairing reduces the original failure rate by half.

## #24 Re: Help Me ! » Conversion of recurring decimal to fraction algebraically » 2019-11-12 21:26:13

Great, the solution of the rational seems to utilize the 0.999...=1 'proof'.

## #25 Re: Help Me ! » Conversion of recurring decimal to fraction algebraically » 2019-11-11 18:57:28

suppose we have A/B = 0.251251251...

A*10//B = 2 remainder A1
A1*10//B = 5 remainder A2
A2*10//B = 1 remainder A3
and A3==A?

Let us check an example of 2/11
A = 2 & B =11
A*10 // B = 1 remainder 9
90 // B = 8 remainder 2=A

so 2/11 = 0.181818......

And you may try primes as A and B and solve 0.251251... out.