US road numbering and math

Neil: How can you take a non-existent road to a city that probably isn't either?
O. J. Grant: Well, there are indeed unlisted numbers. Why not motorways and cities?
- No, it will not work. There must be a better explanation than this.
- The best explanation? Okay, maybe a parallel dimension or a dream, or maybe it is connected with your desire, or you are in a coma after hitting that bucket, or maybe ... maybe you are dead?

Film "Route 60: Cases on the Road", 2002

Math can be seen in many ways that surrounds us every day. There is an opinion that mathematical principles are inextricably linked with what we observe in the Universe surrounding us. The golden ratio, fractals, crystal lattice, a series of Fibonacci numbers. And there is a highway numbering system in the USA. All of you have seen in reality or in the movies, as Americans designate roads in numbers and letters.
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3. And this system was invented in a certain year. And they did it with the help of basic mathematics. The goal was to do this (make it clearer to the inhabitant, as I understood).

In this article we will deal with highways in America. It would seem that such a special need for a map of public roads - put the numbers in order, that's all the complexity. But no, several meanings are hidden in every road name: direction, significance of the road and something else. The system was invented with the help of basic mathematics so that it would be easier for drivers to use the long canvas of American roads.

Some interesting facts

• The numbering scheme for interstate highways was developed by the American Association of National Highways and Transportation in 1957. The current labeling policy has been preserved since 1973.
• Within the boundaries of the North American continent, major highways are designated by numbers less than 100.
• There are no I-60 and I-50 roads in the USA. They had to go through the states with US roads and the same figures, but the repetition of numbers is prohibited by law.
• Previously, the roads had letter suffixes. So labeled long driveways. Under the current law, the roads are no longer marked as such, but until complete liquidation in St. Paul and Minneapolis, I-35E and I-35W remained. The first is heading east from I-35, and the second is heading west, respectively.

For an untrained traveler, a map of the United States may seem confusing, like the metro web of big cities such as New York or London. But if the map is presented in a straightened form, then we will see a geometric grid.



According to the adopted numbering system, even-numbered roads have an east-west direction. For example, I-10, I-90. The lettering “I” in front of the numbers denotes “Interstate” (an interstate road). From the north to the south there are roads with odd signs. For example, I-5, I-95. The numbering increases from the south-west to the north-east direction - from the lower left corner of the map to the upper right. Odd notations are from west to east, and even numbers are from south to north.

Mentioned I-5 is on the West Coast, and I-95 is on the East Coast. It turns out that I-10 is held in Texas, and I-90 in Massachusetts. Major roads are denoted by multiples of five — they increase from north to south, starting with I-5 and ending with I-95.

Interstate highways are paired with primary and are designated by three digits. For example, 290 intersects with the 90th, 495 with the 95th. They can be circular, radial or branching. The three-digit number is formed by adding a digit to the two-digit number of a nearby interstate road: the branches receive an odd digit (190), and the radial and circular ones even number (495). Since the system is invented by man, you can find exceptions to the described patterns.

A lot of information is encrypted in this simple digital scheme. Without a map, you can determine where you are at the moment and where you will get by the number of the road.

Example

Take the road with an arbitrary number 321. This is the road that united one of the main roads and the interstate road number 21. And the road number 21 will be more likely on the west coast than on the east coast.

Guided only by the above set of principles, one can say that one can get from Seattle to Boston via I-90. And if you deviate from the direct path, then, for example, on I-95 to the south you can go to Florida, and then on I-10 to the west to Los Angeles, and, finally, return to Seattle by I-5 to the north.

How it all works

There is a concept of numbers with all their characteristics such as parity, size, number of digits, and so on. Also, people noticed that an object from the real world, such as a highway, also has different properties: direction, location, hierarchical level of importance.

So the authors of the road numbering system tied the properties of the number to the properties of the road object.

Number property	Motorway Parameter
Even Odd	Direction C \ U and B \ W
numerical order	Order Z-V and Yu-S
two digits	interstate highway
three numbers	less significant road joining the interstate

That is the essence of mathematical thinking. It is not about quick arithmetic operations or memorizing formulas, but how to link patterns. Mathematics is a collection of abstract objects that we relate to objects from real life. The use of abstract objects depends entirely on the human imagination.

What else?

Now about the primes.



Small local numbers are supposed to be used for local directions: 2, 3, 5, 7, 11. When all main routes are numbered, smaller roads that connect the main ones with each other can follow the following rule: when combining two directions in the name, you should use their work.

Example

Road 5 connects to road 11, we get direction 55.

And if you get lost on routes with one number, put it in a square, 5 * 5 = 25. This will mean that route 25 connects route 5 with itself. If you connect three roads, it may be a route, for example, 66 - 2 * 3 * 11. Any two numbering of primary roads when multiplied will give a unique number. 33 will never turn out to be a product of two pairs of different designations of main highways. Each number has a unique main factorization.