Rare February tropical disturbance drenching the Florida Keys

By: Dr. Jeff Masters , 13:51 GMT le 06 février 2012

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Our calendars may say it's February, but Mother Nature's calendar says it's more like May in the waters of South Florida, where the year's first significant tropical disturbance is drenching the Keys. The disturbance, designated Invest 90L by NHC late Sunday morning, has dumped 1 - 3 inches of rain over much of the Florida Keys this morning, with Key West receiving 4.34" of rain on Sunday, a record for the date. The storm was close to developing a surface circulation last night, thanks to wind shear values to fell to 20 - 25 knots, and NHC gave 90L a 30% chance of developing into a subtropical depression in a special Tropical Weather Outlook issued last night. However, wind shear has increased to a prohibitive 30 - 40 knots this morning, and 90L is looking much less organized. In their 7 am EST outlook this morning, NHC gave 90L a 0% chance of developing. The system will continue to grow less organized today as it moves over Nassau in the Bahamas and heads out to sea.


Figure 1. Radar-estimated rainfall from Invest 90L.

What's going on?
Obviously, strong tropical disturbances capable of developing into named storms are very rare in February, and I've never seen one in my 30 years as a meteorologist. However, ocean temperatures are warm enough year-round to support a tropical storm in the waters of the Western Caribbean. Water temperatures today in the region were 26 - 26.5°C (79 - 80°F), which is near average for this time of year. If an unusual configuration of the jet stream allows wind shear to drop below about 25 knots in the Western Caribbean, there is the opportunity for a rare off-season tropical storm to form in February. I discussed in an appearance on NPR's All Things Considered on Friday just how unusual the atmospheric flow patterns have been this winter, and today's rare tropical disturbance over South Florida is symptomatic of how whacked-out our 2012 atmosphere has been. In isolation, the strange winter weather of 2011 - 2012 could be a natural rare occurrence, but there have been way too many strange atmospheric events in the past two years for them all to be simply an unusually long run of natural extremes. Something is definitely up with the weather, and it is clear to me that over the past two years, the climate has shifted to a new state capable of delivering rare and unprecedented weather events. Human emissions of heat-trapping gases like carbon dioxide are the most likely cause of such a shift in the climate, as I discussed in my post last week, Where is the climate headed?

A historical precedent: the 1952 Groundhog's Day tropical storm
There is a historical precedent for a tropical storm this time of year--the 1952 Groundhog's Day tropical storm that hit Southwest Florida. According to Wikipedia,

The 1952 Groundhog Day Storm was the only Atlantic tropical cyclone on record in the month of February. First observed in the western Caribbean Sea on February 2, it moved rapidly throughout its duration and struck southwestern Florida within 24 hours of forming. In the state, the winds damaged some crops and power lines, but no serious damage was reported.

Meteorologist Andrew Hagen performed a re-analysis of all the tropical storms between 1944 - 1953 for his Ph.D. thesis, and looked in detail at the 1952 Groundhog Day's storm. He noted that it didn't look like a classic tropical storm, but it didn't look like an extratropical storm, either, and should stay in the database as the first named storm of 1952. In the old teletype files for February 1952, he found a February 2 message from the Cuban Weather Service that expressed some concern about possible tropical development between Cuba and Florida. NHC responded: "TROPICAL STORMS DO NOT FORM IN FEBRUARY."


Figure 2. February 2, 1952 teletype message from the Hurricane Center to the Cuban Weather Service, explaining that there couldn't possibly be a tropical storm in February. Image credit: Andrew Hagen.

Jeff Masters

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Quoting TropicalAnalystwx13:

but puppies don't whine and complain and argue about stupid stuff. They don't worry about how they look or talk back or anything. :P


lol
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting SPLbeater:


for NC? no...lol no....did you write that? *thinks hard*

Nope.

National Weather Service Wilmington, NC.
Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
231. j2008
Quoting TropicalAnalystwx13:

but puppies don't whine and complain and argue about stupid stuff. They don't worry about how they look or talk back or anything. :P
LOL!!! So true.
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Quoting TropicalAnalystwx13:

Actually...

"IF PCP LASTS INTO SAT NIGHT MAY HAVE CONCERN FOR MIXED PCP AS
TEMPS DROP TO NEAR FREEZING BUT DRY AIR SHOULD MAKE IT IN."


for NC? no...lol no....did you write that? *thinks hard*
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting WxGeekVA:


Puppy < Girls..... But girls like puppies so that is a plus.... Just trying to give some advice as someone 3 years ahead of you on the High School timeframe...lol

but puppies don't whine and complain and argue about stupid stuff. They don't worry about how they look or talk back or anything. :P
Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
Quoting hurricanehunter27:
Wow, forgot the fact that I was answering for A. So yes your answer would be correct, but a can also be any number. I think the question should be what is the min not max.


You're right, I needed to take the ray to the first x value OUTSIDE the range - not the last inside.

The algorithm therefore being take the ray out to (102,53) - move one to the left (101,53) - giving

m = (53 - 2) / 101

or 51 / 101

It has been 26 years since I last did maths formally lol.
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Quoting WxGeekVA:
Grothar.... I know you are out there....


he hasnt hid from us for the last 4,378 years he been here..why hide now??
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting SPLbeater:


well, so far i havin no problems. besides, i get to go outside in the early morning to play with the puppy. which actually turns out to a situation where i am trying to get my arm out of its mouth, keep her claws off me and search for safe ground LOL


Puppy < Girls..... But girls like puppies so that is a plus.... Just trying to give some advice as someone 3 years ahead of you on the High School timeframe...lol
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting SPLbeater:
hmmm...GFS forecast low to develop off NE florida, move up E seaboard. Maybe some snow for northeast CONUS...i know i wont get any lol



Actually...

"IF PCP LASTS INTO SAT NIGHT MAY HAVE CONCERN FOR MIXED PCP AS
TEMPS DROP TO NEAR FREEZING BUT DRY AIR SHOULD MAKE IT IN."
Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
Grothar.... I know you are out there....
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting WxGeekVA:


I feel sorry for you dude.... You are missing the best part of your life....


well, so far i havin no problems. besides, i get to go outside in the early morning to play with the puppy. which actually turns out to a situation where i am trying to get my arm out of its mouth, keep her claws off me and search for safe ground LOL
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting RTSplayer:


Like I said, problem must be worded wrong.

There's an infinite number of values for m which meet the criteria, and they range from 1/2 to infinity.

In what you wrote, "a" is never given a definition except that it is some value larger than m.


m = "pi raised to the googleplex power".

it will not hit a lattice point ANYWHERE except 0 = x, but since you defined 0 < x, that isn't a problem.

The only limit you placed on "a" is that it is greater than m, but wait...


m = "pi raised to the googleplex raised to the googleplex"

Also never hits a lattice point, etc.


This is the first week of Calculus 101...or maybe pre-calculus if you take it in high school.

m is a coefficient, which in this case is the slope.

But by the substitution rule, m could be anything. It could be a real number, it could be irrational, it could be another function, etc.


The variable m is given as a range though, so it cannot have an upper bound of infinity since there are plenty of numbers between 1/2 and infinity that can yield integer values for y.

I agree though, there seems to be some missing criteria in the problem. My previous post showed the next highest fraction for m (assuming integer numerators and denominators) that guaranteed non-integer y's, but that isn't the maximum bound. The maximum bound (strictly keeping to integers) would be 100/101, as there is no x in 0 < x < 100 that would yield an integer y. Since 101 is a prime, there is no chance for a reduction to a lower denominator that otherwise potentially yield an integer when being multiplied by x.
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Quoting WxGeekVA:




I'm only in Trig and I only have a C in the class.... Too busy messing with girls in the back row to pay much attention....LOL
Ppppfffttt slacker.
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Quoting chimera245:


I *think* I replied correctly with 50/99.

While it is true that given infinite x there will always be an intercept, the question was actually given:

0 < x <= 100

and

1/2 < m < ??


It's been a few years since A Level maths for me - but I'm fairly certain my argument is correct :)
Quoting chimera245:
I edited my original quick answer - I *think* this is what you are looking for:

Starting with the slope at 0.5, you get intercepts at (2,3), (4,4), (6,5), generally up to ((n-2)*2,n).

Given that your limit of x (n-2)*2 is 100, then the largest one of these intercepts is where n = 52, i.e (100,52).

Moving m upwards moves the x value to the left, so our next intercept point would be (99,52) - this is the limit for m. Back substituting this point using:

m = (y - 2) / x

Gives me

m = (52 - 2) / 99

or 50/99

So I get m < 50/99

Or am I missing something?


The Domain, which is the values of X, are not dependent on the value of m, except to say that x and y cannot both be integers at the same time.

This:

m = (y - 2) / x

Gives me

m = (52 - 2) / 99

or 50/99

So I get m < 50/99




is arbitrary and is not "the" solution, because all you did was plug in arbitrary numbers for x and y, and incorrectly claim that this must be the value of m.

all I have to do to prove your solution wrong is prove that there is at least one solution where m is greater than 50/99 on the domain for 0 < x <= 100, which I already proved there are an infinite number of them.

If you don't believe me, get a graphic calculator and plug it in, or ask a college mathematics professor.


The question, as worded, does not say what either of you think it says.
Member Since: 25 janvier 2012 Posts: 33 Comments: 1520
hmmm...GFS forecast low to develop off NE florida, move up E seaboard. Maybe some snow for northeast CONUS...i know i wont get any lol


Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting Xyrus2000:


50/99 wouldn't be a valid answer. If x is 99, then you wind up with (50/99)*99 = 50.

The first fraction to meet the criteria for m would be 51/101. This is guaranteed to give fractional results over the integer x range as 101 is a prime and greater than the specified range for x.
Wow, forgot the fact that I was answering for A. So yes your answer would be correct, but a can also be any number. I think the question should be what is the min not max.
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Because I never get tired of these:

Member Since: 8 novembre 2009 Posts: 4 Comments: 13801
Quoting WxGeekVA:


I feel sorry for you dude.... You are missing the best part of your life....

LOL yeah.
Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
Quoting SPLbeater:


another good reason why i am homeschooled. i get better grades because i am not distracted by some cute girl. lol(used to happen ALOT)


I feel sorry for you dude.... You are missing the best part of your life....
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting WxGeekVA:




I'm only in Trig and I only have a C+ in the class.... Too busy messing with the girls in the back row to pay much attention....LOL


another good reason why i am homeschooled. i get better grades because i am not distracted by some cute girl. lol(used to happen ALOT)
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Quoting hurricanehunter27:
You are correct sir.


50/99 wouldn't be a valid answer. If x is 99, then you wind up with (50/99)*99 = 50.

The first fraction to meet the criteria for m would be 51/101. This is guaranteed to give fractional results over the integer x range as 101 is a prime and greater than the specified range for x.
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Quoting RTSplayer:


Like I said, problem must be worded wrong.

There's an infinite number of values for m which meet the criteria, and they range from 1/2 to infinity.

In what you wrote, "a" is never given a definition except that it is some value larger than m.


m = "pi raised to the googleplex power".

it will not hit a lattice point ANYWHERE except 0 = x, but since you defined 0 < x, that isn't a problem.

The only limit you placed on "a" is that it is greater than m, but wait...


m = "pi raised to the googleplex raised to the googleplex"

Also never hits a lattice point, etc.


This is the first week of Calculus 101...or maybe pre-calculus if you take it in high school.

m is a coefficient, which in this case is the slope.

But by the substitution rule, m could be anything. It could be a real number, it could be irrational, it could be another function, etc.


Quoting hurricanehunter27:
Well I take AP Geomitry so this is a bit off the trail. Plus I gave it to you how it was worded. Also if you look down I gave you guys 5 possible answers.

50/99 is one of them.


I'm only in Trig and I only have a C in the class.... Too busy messing with girls in the back row to pay much attention....LOL
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting TropicalAnalystwx13:

Yup, that's where I'm gonna try to go.


i hear they have a very good meteorlology class. and a good football team!!!
Member Since: 4 août 2011 Posts: 46 Comments: 4488
210. j2008
Quoting hurricanehunter27:
Most likley you will not experience this type of equation in your life but if you do, I am proud of you.
Like most math above Algebra LOL, unneeded.
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Quoting RTSplayer:


Like I said, problem must be worded wrong.

There's an infinite number of values for m which meet the criteria, and they range from 1/2 to infinity.

In what you wrote, "a" is never given a definition except that it is some value larger than m.


m = "pi raised to the googleplex power".

it will not hit a lattice point ANYWHERE except 0 = x, but since you defined 0 < x, that isn't a problem.

The only limit you placed on "a" is that it is greater than m, but wait...


m = "pi raised to the googleplex raised to the googleplex"

Also never hits a lattice point, etc.


This is the first week of Calculus 101...or maybe pre-calculus if you take it in high school.

m is a coefficient, which in this case is the slope.

But by the substitution rule, m could be anything. It could be a real number, it could be irrational, it could be another function, etc.
Well I take AP Geomitry so this is a bit off the trail. Plus I gave it to you how it was worded. Also if you look down I gave you guys 5 possible answers.

50/99 is one of them.
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My first try with Windows Live Movie Maker. Half way through I realized that I was using visible imagery, meaning everything that happened during the nighttime hours is not shown. Oh well...I'll correct it another time. :P

Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
Quoting hurricanehunter27:
You are correct sir.


Like I said, problem must be worded wrong.

There's an infinite number of values for m which meet the criteria, and they range from 1/2 to infinity.

In what you wrote, "a" is never given a definition except that it is some value larger than m.


m = "pi raised to the googleplex power".

it will not hit a lattice point ANYWHERE except 0 = x, but since you defined 0 < x, that isn't a problem.

The only limit you placed on "a" is that it is greater than m, but wait...


m = "pi raised to the googleplex raised to the googleplex"

Also never hits a lattice point, etc.


This is the first week of Calculus 101...or maybe pre-calculus if you take it in high school.

m is a coefficient, which in this case is the slope.

But by the substitution rule, m could be anything. It could be a real number, it could be irrational, it could be another function, etc.
Member Since: 25 janvier 2012 Posts: 33 Comments: 1520
Quoting SPLbeater:


u shoulda googled it lol


NCSU WOLFPACK!!!!

Yup, that's where I'm gonna try to go.
Member Since: 6 juillet 2010 Posts: 113 Comments: 32831
Quoting j2008:
Ahh I see, cant wait for that(sarcasm)
Most likley you will not experience this type of equation in your life but if you do, I am proud of you.
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204. j2008
Quoting hurricanehunter27:

Read this if your interested to tired to explain. Link
Ahh I see, cant wait for that(sarcasm)
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Quoting chimera245:


I *think* I replied correctly with 50/99.

While it is true that given infinite x there will always be an intercept, the question was actually given:

0 < x <= 100

and

1/2 < m < ??


It's been a few years since A Level maths for me - but I'm fairly certain my argument is correct :)
You are correct sir.
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202. HadesGodWyvern (Mod)
Fiji Meteorological Services
Tropical Disturbance Advisory #3
SEVERE TROPICAL CYCLONE JASMINE (12F)
12:00 PM FST February 7 2012
=====================================

At 0:00 AM UTC, Severe Tropical Cyclone Jasmine, Category Three (955 hPa) located at 17.4S 163.0E has 10 minute sustained winds of 80 knots. The cyclone is reported as moving east southeast at 13 knots. Position poor based on multisatellite enhanced infrared imagery and peripheral surface reports.

Hurricane Force Winds
=====================
30 NM from the center

Storm Force Winds
==================
60 NM from the center

Gale Force Winds
=================
150 NM from the center in northeast quadrant
140 NM from the center in southeast quadrant
110 NM from the center in southwest quadrant
160 NM from the center in northwest quadrant

Overall organization has improved significantly over the past 6 hours with eye forming. System remains in a region of upper diffluence enhanced by a short-wave trough just to the west. Outflow remains good. Cyclone is being steered to the east southeast by strong west-northwest steering and lies in an area of low vertical wind shear.

Dvorak analysis based on dg eye with lg surround

Dvorak Intensity: T5.0/5.0/D1.0/24 HRS

Models generally agree on an east southeastward movement in the next 24 hours.

Forecast and Intensity
=====================

12 HRS: 18.7S 165.6E - 80 knots (CAT 3)
24 HRS: 19.6S 168.1E - 75 knots (CAT 3)
48 HRS: 22.9S 171.6E - 65 knots (CAT 3)

The next tropical disturbance advisory on Severe TC Jasmine from Fiji Meteorological Services will be issued at 8:30 AM UTC..
Member Since: 24 mai 2006 Posts: 52 Comments: 46915
Quoting RTSplayer:
The question placed no conditions on the value of y,


I *think* I replied correctly with 50/99.

While it is true that given infinite x there will always be an intercept, the question was actually given:

0 < x <= 100

and

1/2 < m < ??


It's been a few years since A Level maths for me - but I'm fairly certain my argument is correct :)
Member Since: Posts: Comments:
Quoting j2008:
Ha you got a few options there. DEATH BY MATH JK. Your doing that and your a freshman? Wow what type of math is that? , (Havnt seen that stuff yet in my HS life)

Read this if your interested to tired to explain. Link
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Quoting hurricanehunter27:
For all you guys that tried to help me. THANK YOU. Means a lot that you guys will take time to help me.


u shoulda googled it lol
Quoting hurricanehunter27:
So got collages in mind?



NCSU WOLFPACK!!!!
Member Since: 4 août 2011 Posts: 46 Comments: 4488
Ok, I can prove intuitively that the limit really is infinity.

The question placed no conditions on the value of y, except that the line never passes through a lattice point, which is to say y and x cannot both be integers at the same time.

so, for example:

y = mx - 2, 0 < x < 100, and (1 / 2) < m < a.

if m = pi, then no lattice point will ever be crossed for any x = / = 0, and m > 0.5.


And now, if we replace "m" with some function of pi, such as 2 * pi, 3 * pi, 4 * pi, etc, none of those will ever cross a lattice point either.

Infact, for n * pi as n approaches infinity, the line will also never cross any lattice point.


So a has no maximum limit except "infinity".

m does have a MINIMUM limit which is infinitesmally close to 1/2, but only because he defined 1 / 2 < m. A has a minimum limit infinitesmally close to m.


There are an infinite number of values for m which do not violate any of the conditions as they were given in the problem.

Edit:

Wow.

This site really doesn't handle basic mathematics symbols very well. HTML and scripting languages use the less than and greater than and slashes for tags and interupts and the script can't handle it.


P.S.

Your teacher/boss and your text book answer key can be wrong.

Happens all the time in college and at work.
Member Since: 25 janvier 2012 Posts: 33 Comments: 1520
197. HadesGodWyvern (Mod)
Fiji Meteorological Services
Tropical Disturbance Advisory #4
TROPICAL CYCLONE CYRIL (11F)
12:00 PM FST February 7 2012
===================================

A TROPICAL CYCLONE ALERT IS NOW IN FORCE FOR NIUE.

A STRONG WIND WARNING REMAINS IN FORCE FOR NIUE.

At 0:00 AM UTC, Tropical Cyclone Cyril, Category Two (985 hPa) located at 20.0S 171.9W has 10 minute sustained winds of 50 knots. The cyclone is reported as moving east southeast at 18 knots. Position fair based on hourly GMS enhanced infrared radar imagery and peripheral surface reports.

Storm Force Winds
===================
20 NM from the center

Gale Force Winds
===============
120 NM from the center in northeast quadrant
120 NM from the center in southeast quadrant
120 NM from the center in northwest quadrant
50 NM from the center in southwest quadrant

Organization has improved significantly past 24 hours. Convection increased with primary bands trying to trap around the low level circulation center. System lies south of 250 HPA ridge axis. Outflow good to the north and east. System lies in a low to moderate sheared environment and is being steered southeast by a northwest deep layer mean flow into an area of increasing shear. Sea surface temperature around 27C

Dvorak analysis based on 0.9 wrap

Dvorak Intensity: T3.5/3.5/D1.5/24 HRS

Global models move the system southeastward with decreasing intensification.

Forecast and Intensity
=======================

12 HRS: 22.2S 168.9W - 45 knots (CAT 1)
24 HRS: 24.8S 165.0W - 40 knots (CAT 1)

The next tropical disturbance advisory from Fiji Meteorological Services on TC Cyril will be issued at 8:30 AM UTC..
Member Since: 24 mai 2006 Posts: 52 Comments: 46915
196. j2008
Quoting WxGeekVA:


Penn State, Miami (FL), Ohio State, Florida State, and Oklahoma.
Ha you got a few options there.
Quoting hurricanehunter27:
A lattice point in an xy-coordinate systems is any point (x,y) where x and y are both integers. The
graph of y = mx + 2 passes through no lattice point with 0 < x < (or equal to 100) for all m such that 1/2< m < a .
What is the maximum possible value of a?


Sry had to re-type that.
DEATH BY MATH JK. Your doing that and your a freshman? Wow what type of math is that? , (Havnt seen that stuff yet in my HS life)
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Quoting WxGeekVA:


Penn State, Miami (FL), Ohio State, Florida State, and Oklahoma.
Got a letter from Miami today lol. I am planning if I can keep my grades up to go to Rice, Emory, or UGA.
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Quoting hurricanehunter27:
So got collages in mind?


Penn State, Miami (FL), Ohio State, Florida State, and Oklahoma.
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting WxGeekVA:


Junior.
So got collages in mind?
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Quoting hurricanehunter27:
Lol what grade you in? Im a freshman.


Junior.
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting WxGeekVA:
I just got on here to get away from math homework, and guess what I see? COMPLICATED MATH!!!! ARRRRGH!!!!
Lol what grade you in? Im a freshman.
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I just got on here to get away from math homework, and guess what I see? COMPLICATED MATH!!!! ARRRRGH!!!!
Member Since: 3 septembre 2011 Posts: 13 Comments: 3477
Quoting TheoJesse:
#173 Nea.
Is there any explanations of what the colors represent?
Jesse
Yes. Those show ice concentration. Lime green denotes land; solid blue is open water (0% ice). The rest of the colors range from blues and greens (thinner ice) to yellows, reds, and magentas (thicker ice).
Member Since: 8 novembre 2009 Posts: 4 Comments: 13801
Quoting hurricanehunter27:
For all you guys that tried to help me. THANK YOU. Means a lot that you guys will take time to help me.

No Problem.
Anytime!

:):))
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For all you guys that tried to help me. THANK YOU. Means a lot that you guys will take time to help me.
Member Since: Posts: Comments:
Quoting chimera245:
I edited my original quick answer - I *think* this is what you are looking for:

Starting with the slope at 0.5, you get intercepts at (2,3), (4,4), (6,5), generally up to ((n-2)*2,n).

Given that your limit of x (n-2)*2 is 100, then the largest one of these intercepts is where n = 52, i.e (100,52).

Moving m upwards moves the x value to the left, so our next intercept point would be (99,52) - this is the limit for m. Back substituting this point using:

m = (y - 2) / x

Gives me

m = (52 - 2) / 99

or 50/99

So I get m < 50/99

Or am I missing something?
I love you. (Net hug)
Member Since: Posts: Comments:
I edited my original quick answer - I *think* this is what you are looking for:

Starting with the slope at 0.5, you get intercepts at (2,3), (4,4), (6,5), generally up to ((n-2)*2,n).

Given that your limit of x (n-2)*2 is 100, then the largest one of these intercepts is where n = 52, i.e (100,52).

Moving m upwards moves the x value to the left, so our next intercept point would be (99,52) - this is the limit for m. Back substituting this point using:

m = (y - 2) / x

Gives me

m = (52 - 2) / 99

or 50/99

So I get m < 50/99

Or am I missing something?
Member Since: Posts: Comments:

Looks to me like things are slow on this blog today.
Well, here is what is going on right here.
And IT AINT SLOW.....

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Quoting chimera245:


Consider that a slope of 1/2 would imply an intercept at (2,3) (y = (0.5 * 2) + 2), the next intercept with a slope > 0.5 would be (1,3). Rearranging to m = (y - 2) / x gives:

m = (3 - 2) / 1

therefore max value of a is 1.


Ok, he wants the line to never pass through a lattice point between 0 < X < 100.

If m is rational and between 100 and 1/100, then the line will always pass through a lattice point, eventually.
Member Since: 25 janvier 2012 Posts: 33 Comments: 1520

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