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#2 Euler Avenue » Formula for ratio of weights at different latitudes » 2011-09-01 07:14:39

JaneFairfax
Replies: 2

As you know, the Earth is not a perfect sphere so a person’s weight varies from place on place on the surface of the globe. Assuming that the Earth is an ellipsoid (that is, the intersection of the Earth with a plane passing through the Poles is an ellipse) then the person’s weight depends only on which latitude he or she is on.


Suppose he/she weighs
at latitude
N or S. Then his/her weight
at latitude
N or S is given by the following formula, which I calculated today: big_smile

[align=center]

[/align]

where

is the ratio of the Equatorial radius of the Earth to the Polar radius of the Earth.

Notes:

(1)

.

(2)

and
are weights, not masses. The person’s mass does not vary with location on Earth.

(3) Because the left-hand side is a ratio, it does not matter which unit you use to measure weight. You can use newtons, pounds, stones, or even the unscientific kilos. The utility of the formula is that if you know your weight at a particular latitude on Earth, you can calculate your weight at any other latitude on Earth. cool

#3 Jokes » How do you pronounce “Le-a”? » 2011-07-14 21:51:40

JaneFairfax
Replies: 6

This had me falling over laughing. roflol

[align=center]tumblr_l13mbg6QlF1qb5gkjo1_500.png[/align]

#4 Re: Jokes » Random jokes I come across » 2011-06-14 01:12:16

A dissatisfied train passenger writes the following letter of complaint to the railway authorities: "Gentlemen: I have been riding your trains daily for the last 22 years and the service on your line seems to be getting worse every day. I am tired of standing in the aisle all the time on my way to and from work. I think your transportation system is worse than that enjoyed by people 2000 years ago. Yours truly, A Commuter."

The railway authorities reply: "Dear Sir: We received your letter with reference to the shortcomings of our service and believe you are somewhat confused in your history. The only mode of transportation 2000 years ago was by foot. Sincerely, Western Railways."

The passenger replies back: "Gentlemen: I am in receipt of your letter and I think you are the ones who are confused in your history. If you refer to the Old Testament book of David in the Bible, Chapter Nine, you will find that Balaam rode to town 'seated' on his donkey. That, gentlemen, is something I have not been able to do on your trains in the last 22 years. Yours truly, A Long 'Standing' Commuter."

#5 Jokes » Random jokes I come across » 2011-06-14 00:59:51

JaneFairfax
Replies: 267

A concerned husband went to a doctor to talk about his wife. "Doctor, I think my wife is deaf because she never hears me the first time and I always have to repeat myself."

"Well," the doctor replied, "go home tonight and stand about 5 metres from her and say something to her. If she doesn't hear, move a metre closer and say it again. Keep doing this so we'll get an idea of the severity of her deafness."

The husband goes home and does what the doctor instructed. He stands 5 metres from his wife as she is chopping some vegetables and says, "Honey, what's for dinner?"

Hearing no response, he moves a metre closer and asks again. No reply. He moves another metre closer and still no reply. Fed up, he moves right behind her and asks again, "Honey, what's for dinner?"

She replies, "For the fourth time, vegetable stew!"

#6 Re: Dark Discussions at Cafe Infinity » Nokia and Apple settle patent dispute » 2011-06-14 00:53:28

Oh, okay. No problem. I should learn to phrase my sentences more carefully next time to avoid misunderstandings. smile

#8 Dark Discussions at Cafe Infinity » Nokia and Apple settle patent dispute » 2011-06-13 21:24:11

JaneFairfax
Replies: 6

Nokia has announced that Apple has agreed to pay royalties for use of its technologies, ending the long-running legal dispute between the two firms. The Finnish company sued Apple for patent infringements in 2009 but Apple in turn accused Nokia of infringing its patents. It is good to see the Americans finally admitting that they are wrong and agreeing to settle up.

http://z8.invisionfree.com/DYK/index.php?showtopic=924

#9 Help Me ! » Number-theory problem (from another forum) » 2011-06-09 04:10:57

JaneFairfax
Replies: 21

The following problem was posted by someone else on another forum but has not received any reply on that forum. I’m re-posting it here so people here can have a crack at it. smile

#10 Re: Help Me ! » Linear algebra : Linear independence » 2011-05-31 22:35:26

The second question means: Prove that one of the matrices can be written as a linear combination of the others. (You just rewrite the equation you found in the first question.)

#12 Re: Introductions » Getting Started » 2011-05-17 03:08:32

Hi jyoticse804! Welcome to the forum. wave

#13 Re: Introductions » Hi all... » 2011-05-17 03:07:20

Hi Deon588! Welcome to the forum. wave

#14 Re: Introductions » hay » 2011-05-17 03:06:20

Hi *67! Welcome to the forum. wave

#15 Re: Introductions » Hello to all » 2011-05-17 03:04:22

Hi Jlo! Welcome to the forum. wave

#16 Re: Introductions » New here » 2011-05-17 02:43:44

Hi Googl! Welcome to the forum. wave

#17 Re: Introductions » Hello! New Member Here » 2011-05-17 02:35:52

Hi calculatewhat! Welcome to the forum. wave

#18 Re: Help Me ! » Ideals » 2011-05-03 00:12:15

is a principal-ideal domain (PID) so all its ideals are principally generated. However note that
in
so not all the ideals you listed are distinct.

To test for maximality, consider ideals

where n is a prime divisor of 12. What happpens if n does not divide 12 or is a non-prime divisor thereof?

#19 Re: Exercises » Group Theory » 2011-05-02 23:27:58

Ricky wrote:

(It may be noted that matrices of integers are groups).

Are you sure? Or have I misunderstood something here? yikes

#20 Help Me ! » Ricky, I need your help » 2011-01-22 02:38:22

JaneFairfax
Replies: 2

Well, anyone who knows about Galois theory can help me here. smile


I’m trying to construct finite fields with
elements, where p is a prime and n > 1 is an integer. I’ve come up with

[align=center]

[/align]

i.e. the quotient ring of the ring of polynomials over the field of integers modulo p by the principal ideal generated by

, an irreducible polynomial of degree n. The ideal generated by the irreducible polynomial is maximal; since it is also a proper ideal, the quotient ring must be a field. A typical element in it has the form
,
; there are p possible values for
for each
and so there are
elements altogether. Hence it’s a finite field with
elements.

Now my question is: given any p and any n (> 1), can we always find an irreducible polynomial of degree n in

? Ricky? Anyone? neutral

#21 Re: Exercises » Jane’s Exercises III » 2011-01-22 02:21:41

I forgot about #6. Thanks, scientia. smile

Next question is on algebraic topology.


#22 Re: Dark Discussions at Cafe Infinity » This is funny » 2010-12-30 03:49:36

Sorry, Tigeree. smile The fact is that I’ve never seen the Australians playing so badly before. Ricky Ponting may or may not be to blame, but the statistics are there for all to see. Before Ponting became test captain in 2004, Australia had won eight Ashes series in a row. Since he took on the captaincy role, however, Australia have failed to win the Ashes in three of the last four series. Coincidence? roll

#23 Dark Discussions at Cafe Infinity » This is funny » 2010-12-26 04:47:18

JaneFairfax
Replies: 3

The Ashes 2010–11, Fourth Test, Melbourne. End of Day 1: Australia all out for 98, England no wickets for 157! roflol

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