3176: Inverted Catenaries - Revision history

Elektrizikekswerk: /* Explanation */

2026-02-04T10:16:20Z

‎Explanation

Elektrizikekswerk: /* Explanation */ Removed winter tire explanation again (not really relevant) but provided wiki link instead.

2026-01-30T09:59:38Z

‎Explanation: Removed winter tire explanation again (not really relevant) but provided wiki link instead.

BunsenH: /* Explanation */ explain winter tires

2026-01-29T22:13:19Z

‎Explanation: explain winter tires

Elektrizikekswerk: /* Explanation */ No reason for tag given. Explanation seems complete, removed tag. Added some sort of interpretation of the comic.

2026-01-12T12:01:26Z

‎Explanation: No reason for <incomplete> tag given. Explanation seems complete, removed tag. Added some sort of interpretation of the comic.

Utdtutyabthsc: /* Transcript */

2025-12-22T07:07:41Z

‎Transcript

Zagorath: /* Explanation */ clarify the tyre changes are on cars

2025-12-13T13:05:36Z

‎Explanation: clarify the tyre changes are on cars

2600:6C5A:58F0:66A0:54A7:36B9:6A52:C682: Reversed my previous edit and added "(presumably from an "inverted canary tree")"

2025-12-09T02:28:07Z

Reversed my previous edit and added "(presumably from an "inverted canary tree")"

2600:6C5A:58F0:66A0:54A7:36B9:6A52:C682: I added "in the street" to the transcription.

2025-12-09T02:25:51Z

I added "in the street" to the transcription.

82.13.184.33: /* Explanation */

2025-12-08T09:53:06Z

‎Explanation

174.53.211.85: /* Explanation */

2025-12-07T00:29:33Z

‎Explanation

@@ Line 16: / Line 16: @@
 The title text mentions all-shape tires (as a play on all-season tires), which are advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally use wheels pasted together from pieces of an equiangular spiral. The all-shape tire is said to wear out very quickly like low quality all-season tires used to. (The best modern all-season tires perform better than the average winter tire and have a 62k mile warranty.)
-The comic might be a comment on the aforementioned experiments. While mathematically interesting and a good example of experimental mathematics (see [[3180]]) the "real live" applications of this are rather... limited. At least in this literal form.
+The comic might be a comment on the aforementioned experiments. While mathematically interesting and a good example of experimental mathematics (see [[3180]]) the "real life" applications of this are rather... limited. At least in this literal form.
 ==Transcript==

@@ Line 10: / Line 10: @@
 ==Explanation==
-During the winter, in snowy / icy areas, people may replace their car's summer or all-season tires with winter tires made specifically for the cold environment. (Winter tires are made of more flexible materials, have deeper treads, and/or use studs for traction. However, softer materials lead to increased wear, and studs are banned from some roads, so people who use winter tires usually swap them back to regular tires after the snow and ice have gone for the year.) In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
+During the winter, in snowy / icy areas, people may replace their car's summer or all-season tires with {{w|Snow tires}} made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
 Note, however, that this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation would also restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems. Letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.

@@ Line 10: / Line 10: @@
 ==Explanation==
-During the winter, in snowy areas, people may replace their car's summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
+During the winter, in snowy / icy areas, people may replace their car's summer or all-season tires with winter tires made specifically for the cold environment. (Winter tires are made of more flexible materials, have deeper treads, and/or use studs for traction. However, softer materials lead to increased wear, and studs are banned from some roads, so people who use winter tires usually swap them back to regular tires after the snow and ice have gone for the year.) In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
 Note, however, that this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation would also restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems. Letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.

@@ Line 10: / Line 10: @@
 ==Explanation==
 During the winter, in snowy areas, people may replace their car's summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
@@ Line 17: / Line 15: @@
 The title text mentions all-shape tires (as a play on all-season tires), which are advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally use wheels pasted together from pieces of an equiangular spiral. The all-shape tire is said to wear out very quickly like low quality all-season tires used to. (The best modern all-season tires perform better than the average winter tire and have a 62k mile warranty.)
 ==Transcript==

@@ Line 20: / Line 20: @@
 ==Transcript==
 {{incomplete transcript|Don't remove this notice too soon.}}
-:[Megan and Cueball are walking together as inverted catenary curves fall from the sky (presumably from an "inverted canary tree"). A few have landed in a regular formation, all flat-side down and evenly spaced, with some touching each other.]
+:[Megan and Cueball are walking together as inverted catenary curves fall from the sky (presumably from an "inverted catenary tree"). A few have landed in a regular formation, all flat-side down and evenly spaced, with some touching each other.]
 :Cueball: Oh wow, the first inverted catenary fall of the year!
 :Cueball: Time to swap out my all-season tires for square ones.

@@ Line 12: / Line 12: @@
 {{incomplete|This page was created BY A TRAPEZOIDAL WHEEL. Don't remove this notice too soon.}}
-During the winter, in snowy areas, people may replace their summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
+During the winter, in snowy areas, people may replace their car's summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
 Note, however, that this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation would also restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems. Letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.

@@ Line 12: / Line 12: @@
 {{incomplete|This page was created BY A TRAPEZOIDAL WHEEL. Don't remove this notice too soon.}}
-During the winter, in snowy areas, traditionally people need to replace their summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary are capable of rolling smoothly, contrary to how they would act on a normal road. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
+During the winter, in snowy areas, people may replace their summer or all-season tires with winter tires made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary are capable of rolling smoothly, contrary to how they would act on a normal road. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.
 Mathematicians have found [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html what types of roads would suit weird wheels the most], and inverted catenary curves are best suited for a square wheel. People have made real tracks demonstrating this.
-Note however, this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation also would restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems, but letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.
+Note, however, that this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation also would restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems. Letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.
-The title text mentions all-shape tires (as a play on all-season tires), which is advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally require wheels pasted together from pieces of an equiangular spiral. The all-shape wheel is said to wear out very quickly like low quality all-season used to. (The best modern all-season tires perform better than the average winter tire and have a 62k mile warranty)
+The title text mentions all-shape tires (as a play on all-season tires), which are advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally use wheels pasted together from pieces of an equiangular spiral. The all-shape tire is said to wear out very quickly like low quality all-season tires used to. (The best modern all-season tires perform better than the average winter tire and have a 62k mile warranty.)
 ==Transcript==