Bayoubill’s Ongoing Ponderance of the “Four-Corners” Question

[bayoubill]

The states of Colorado, Utah, Arizona, and New Mexico all meet at a common point, popularly referred to as “Four Corners”.

This point is analogous to the “origin” (i.e., “0”) on a two-dimensional X-Y Cartesian plane. (You may recall from elementary algebra that the Cartesian plane is separated, by way of the X and Y axes, into four separate regions that meet at the origin.)

so...

Question 1: Do the States of Colorado and Arizona touch each other…?

Question 2: Do the States of Utah and New Mexico touch each other…?

Question 3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

 

[deaddogseye]

According to wikipedia



The United States first acquired the area now called Four Corners from Mexico after the Mexican–American War in 1848. In 1863 Congress created Arizona Territory from the western part of New Mexico Territory. The boundary was defined as a line running due south from the southwest corner of Colorado Territory, which had been created in 1861. This was an unusual act of Congress, which almost always defined the boundaries of new territories as lines of latitude or longitude, or following rivers. By defining one boundary as starting at the corner of another Congress ensured the eventual creation of four states meeting at a point, regardless of the inevitable errors of boundary surveying.[1] The area was first surveyed by the U.S. Government in 1868 as part of an effort to make Colorado Territory into a state, the first of the Four Corners states formed. The first marker was placed at the spot in 1912.[2] The first Navajo tribal government was established in 1923 to regulate an increasing number of oil exploration activities on Navajo tribal lands.[3]

and remember -- you read it on the internet so it must be true.

 

[Peach]

The states of Colorado, Utah, Arizona, and New Mexico all meet at a common point, popularly referred to as “Four Corners”.

This point is analogous to the “origin” (i.e., “0”) on a two-dimensional X-Y Cartesian plane. (You may recall from elementary algebra that the Cartesian plane is separated, by way of the X and Y axes, into four separate regions that meet at the origin.)

so...

Question 1: Do the States of Colorado and Arizona touch each other…?

Question 2: Do the States of Utah and New Mexico touch each other…?

Question 3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

The points converge.

 

[bayoubill]

According to wikipedia



The United States first acquired the area now called Four Corners from Mexico after the Mexican–American War in 1848. In 1863 Congress created Arizona Territory from the western part of New Mexico Territory. The boundary was defined as a line running due south from the southwest corner of Colorado Territory, which had been created in 1861. This was an unusual act of Congress, which almost always defined the boundaries of new territories as lines of latitude or longitude, or following rivers. By defining one boundary as starting at the corner of another Congress ensured the eventual creation of four states meeting at a point, regardless of the inevitable errors of boundary surveying.[1] The area was first surveyed by the U.S. Government in 1868 as part of an effort to make Colorado Territory into a state, the first of the Four Corners states formed. The first marker was placed at the spot in 1912.[2] The first Navajo tribal government was established in 1923 to regulate an increasing number of oil exploration activities on Navajo tribal lands.[3]

and remember -- you read it on the internet so it must be true.

this tells me nothing I didn't already know...

I already said the corners of the four states meet at a common point...


the questions remain:

1: Do the States of Colorado and Arizona touch each other…?

2: Do the States of Utah and New Mexico touch each other…?

3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

 

[bayoubill]

The states of Colorado, Utah, Arizona, and New Mexico all meet at a common point, popularly referred to as “Four Corners”.

This point is analogous to the “origin” (i.e., “0”) on a two-dimensional X-Y Cartesian plane. (You may recall from elementary algebra that the Cartesian plane is separated, by way of the X and Y axes, into four separate regions that meet at the origin.)

so...

Question 1: Do the States of Colorado and Arizona touch each other…?

Question 2: Do the States of Utah and New Mexico touch each other…?

Question 3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

The points converge.

and then do what...?


asymptotes also converge, infinitely close but never quite touching...

 

[Peach]

According to wikipedia



The United States first acquired the area now called Four Corners from Mexico after the Mexican–American War in 1848. In 1863 Congress created Arizona Territory from the western part of New Mexico Territory. The boundary was defined as a line running due south from the southwest corner of Colorado Territory, which had been created in 1861. This was an unusual act of Congress, which almost always defined the boundaries of new territories as lines of latitude or longitude, or following rivers. By defining one boundary as starting at the corner of another Congress ensured the eventual creation of four states meeting at a point, regardless of the inevitable errors of boundary surveying.[1] The area was first surveyed by the U.S. Government in 1868 as part of an effort to make Colorado Territory into a state, the first of the Four Corners states formed. The first marker was placed at the spot in 1912.[2] The first Navajo tribal government was established in 1923 to regulate an increasing number of oil exploration activities on Navajo tribal lands.[3]

and remember -- you read it on the internet so it must be true.

this tells me nothing I didn't already know...

I already said the corners of the four states meet at a common point...


the questions remain:

1: Do the States of Colorado and Arizona touch each other…?

2: Do the States of Utah and New Mexico touch each other…?

3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

At a single point, all are together. Draw a line from Colorado to the point, and you will reach Arizona.

 

[bayoubill]

According to wikipedia



The United States first acquired the area now called Four Corners from Mexico after the Mexican–American War in 1848. In 1863 Congress created Arizona Territory from the western part of New Mexico Territory. The boundary was defined as a line running due south from the southwest corner of Colorado Territory, which had been created in 1861. This was an unusual act of Congress, which almost always defined the boundaries of new territories as lines of latitude or longitude, or following rivers. By defining one boundary as starting at the corner of another Congress ensured the eventual creation of four states meeting at a point, regardless of the inevitable errors of boundary surveying.[1] The area was first surveyed by the U.S. Government in 1868 as part of an effort to make Colorado Territory into a state, the first of the Four Corners states formed. The first marker was placed at the spot in 1912.[2] The first Navajo tribal government was established in 1923 to regulate an increasing number of oil exploration activities on Navajo tribal lands.[3]

and remember -- you read it on the internet so it must be true.

this tells me nothing I didn't already know...

I already said the corners of the four states meet at a common point...


the questions remain:

1: Do the States of Colorado and Arizona touch each other…?

2: Do the States of Utah and New Mexico touch each other…?

3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

At a single point, all are together. Draw a line from Colorado to the point, and you will reach Arizona.

if you thus have Colorado connected to Arizona, you will have created a barrier that prevents Utah from touching New Mexico...

 

[Peach]

this tells me nothing I didn't already know...

I already said the corners of the four states meet at a common point...


the questions remain:

1: Do the States of Colorado and Arizona touch each other…?

2: Do the States of Utah and New Mexico touch each other…?

3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

At a single point, all are together. Draw a line from Colorado to the point, and you will reach Arizona.

if you thus have Colorado connected to Arizona, you will have created a barrier that prevents Utah from touching New Mexico...

Only if you stop. Thus, walk it & let the board know. ; )

 

[bayoubill]

At a single point, all are together. Draw a line from Colorado to the point, and you will reach Arizona.

if you thus have Colorado connected to Arizona, you will have created a barrier that prevents Utah from touching New Mexico...

Only if you stop. Thus, walk it & let the board know. ; )

I'm not sure you understand the question...

you seem to be taking about something else entirely...

 

[del]

sad when cousins marry

 

[Warrior102]

BBill - your apology on Hannity.
Sickening dude.
Get some self respect.

 

[Amelia]

The states of Colorado, Utah, Arizona, and New Mexico all meet at a common point, popularly referred to as “Four Corners”.

This point is analogous to the “origin” (i.e., “0&#8221 on a two-dimensional X-Y Cartesian plane. (You may recall from elementary algebra that the Cartesian plane is separated, by way of the X and Y axes, into four separate regions that meet at the origin.)

so...

Question 1: Do the States of Colorado and Arizona touch each other…?

Question 2: Do the States of Utah and New Mexico touch each other…?

Question 3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

I'll say no.



Now can you help me with my ongoing ponderance - is a human being locally Euclidean?

 

[bayoubill]

BBill - your apology on Hannity.
Sickening dude.
Get some self respect.

I appreciate the reality check, W...

I wanted to send you a PM to discuss things, but I got this message:

Warrior102 has chosen not to receive private messages or may not be allowed to receive private messages. Therefore you may not send your message to him/her.


Is there any other way you and I could continue our discussion in private...?

 

[bayoubill]

The states of Colorado, Utah, Arizona, and New Mexico all meet at a common point, popularly referred to as “Four Corners”.

This point is analogous to the “origin” (i.e., “0”) on a two-dimensional X-Y Cartesian plane. (You may recall from elementary algebra that the Cartesian plane is separated, by way of the X and Y axes, into four separate regions that meet at the origin.)

so...

Question 1: Do the States of Colorado and Arizona touch each other…?

Question 2: Do the States of Utah and New Mexico touch each other…?

Question 3: If you answered “yes” to Questions 1 & 2, please explain how this is possible.

I'll say no.



Now can you help me with my ongoing ponderance - is a human being locally Euclidean?

intriguing question, Steph... give us some background...

 

[asaratis]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Imagine drawing the corner of one state with a pen of zero width. No matter which state boundary you try to trace around that corner, you have to pass directly over the corner spot (in order to start moving your pencil perpendicular to the line you just traced to get to the corner) THEREFORE: The corner point is shared by all four states.

 

[Amelia]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Well said. Except I went the other direction in my answer. I went with it belonging to none of them.

Has anyone looked at the issue legally? Does the border between two states belong to each state? Or to neither?

 

[bayoubill]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Imagine drawing the corner of one state with a pen of zero width. No matter which state boundary you try to trace around that corner, you have to pass directly over the corner spot (in order to start moving your pencil perpendicular to the line you just traced to get to the corner) THEREFORE: The corner point is shared by all four states.

It is understood and accepted that all four states share the common point...

consider this though... if Colorado and Arizona are in contact with each other,

it therefore creates a barrier that prevents Utah and New Mexico from making contact...

 

[bayoubill]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Well said. Except I went the other direction in my answer. I went with it belonging to none of them.

Has anyone looked at the issue legally? Does the border between two states belong to each state? Or to neither?

funny thing... my musings have caused me to wonder whether states that border each other actually touch...

do two regions on opposite sides of a zero axis actually touch each other...?

 

[007]

sad when cousins marry

I just wanna know why the OP keeps picking his fucking nose.

 

[Amelia]

I say all four states share that corner spot (a single point) ....thus each touches the other three. No matter how narrow the lines are, the corner point is the same width. The corner point must belong to all four states or it must belong to none of them.

Well said. Except I went the other direction in my answer. I went with it belonging to none of them.

Has anyone looked at the issue legally? Does the border between two states belong to each state? Or to neither?

funny thing... my musings have caused me to wonder whether states that border each other actually touch...

do two regions on opposite sides of a zero axis actually touch each other...?

zero axis?


Mathematically, the four quadrants defined by the intersection of the x-axis and y-axis do not touch each other. The axes are not part of the quadrants. Removal of the axes from the set of points making up the xy-plane results in 4 disconnected regions.