Silly U.S. Map Puzzle #5

What do the colors on this map mean?

mappuzzle5

If you wish to check your answer, or just what to know what the solution is, just scroll down.

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Solution:

Of the other 49 states in the USA, how many are adjacent to this one? The answer to this question determines the color of each state.

One point of clarification: if it takes a lengthy trip by boat or ship to get there, I didn’t count it as an adjacent state . . . so, for example, Minnesota and Michigan didn’t make each other’s lists. Simply going over a bridge isn’t enough for this sort of separation, though, which is why Arkansas and Tennessee did make each others’ lists of adjacent states. Had I interpreted water borders differently, this map would have some differences.

Another way this map could be altered would be to count states that meet others only at a single point, rather than a border with non-zero length. This would change the colors of the “four corners” states of Arizona, Utah, New Mexico, and Colorado, but would have no effect on the other 46 states.

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Silly U.S. Map Puzzles #4a and 4b

First, for puzzle #4a, what are the meanings of the colors on this map?

mapquiz4a-letters

For puzzle #4b, what do the colors mean on this second, similar map?

mapquiz4b-characters

To find the answers, simply scroll down.

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Solution:

In the first map, consider the number of letters in the name of each state. Is this number prime or composite?

In the second map, consider the number of characters, rather than letters, in each state’s name. This number is different for states with two-word names, due to the single character, a blank space, needed to separate the two words. Again: prime, or composite?

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Silly U.S. Map Puzzle #3

What is represented by the colors on this map?

mapquiz3

The answer may be found by scrolling down.

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Answer:

Do any of the borders of this state contain squiggles? (Note: if you think New Mexico is the wrong color, check the part of that state which borders El Paso, Texas.)

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Silly U.S. Map Puzzle #2

What is represented by the colors on this map?

mapquiz2

If you give up, you can scroll down to find the answer.

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Answer: the colors show whether the name of each state starts with a letter in the first, or second, half of the alphabet.

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Silly U.S. Map Puzzle #1

What is represented by the colors on this map?

mapquiz1

If you decide to give up, you can scroll down for the answer . . . but, I promise, the solution to this puzzle is extremely simple.

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Keep scrolling, if you’re looking for the answer….

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Answer:

The map shows how many words are in the name of each state.

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Earth’s Oceans’ and Continents’ Relative Surface Areas, Analyzed, with Two Pie Charts

I’ll start this analysis with a simple land/water breakdown for Earth’s surface:

land and water

The two figures in the chart above are familiar figures for many — but how does “land” break down into continents, and how does “water” break down into oceans, as fractions of Earth’s total surface area? That’s what this second chart shows.

continents and oceans

With continents, I placed them on the chart to make it easier to see physically-connected continents as sets of adjacent wedges of similar color, separated only by thin lines. The most obvious example of this is Europe and Asia, which are considered separate continents in the first place only for historical reasons, not geographical ones. Combine them, into Eurasia, and it has 36.3% of Earth’s total land area, which is (36.3%)(0.292) = 10.6% of Eath’s total surface area. Even then, Earth’s three largest oceans (the Atlantic, Indian, and Pacific Oceans) are each larger than Eurasia.

There are other naturally-connected continents, albeit with much smaller land connections — narrow enough for humans to have altered this fact, only a “blip” ago on geographical time-scales, by building the Suez and Panama Canals. In the case of the Suez, its construction severed, artificially, the naturally-occurring land connection between Eurasia and Africa, and the term “Afro-Eurasia” has been used for the combination of all three traditionally-defined continents. Afro-Eurasia has 56.7% of Earth’s land, but that’s only (56.7%)(0.292) = 16.6% of Earth’s total surface area. That’s larger than the Indian Ocean, at (19.5%)(0.708) = 13.8% of Earth surface area. However, both the Atlantic Ocean, at (23.5%)(0.708) = 16.6% of Earth’s surface area, and the Pacific Ocean, at (46.6%)(0.708) = 33.0% of Earth’s surface area, are still larger than Afro-Eurasia.

The Pacific Ocean alone, in fact, has a greater surface area than all of Earth’s land — combined.

The other case that can be made for continent-unification involves North and South America, since their natural land connection was severed, only about a century ago, by the construction of the Panama Canal. Combine the two, and simply call the combination “the Americas,” and that’s 28.5% of earth’s land, which is (28.5%)(0.292) = 8.3% of Earth’s surface area. (I didn’t simply call this combination “America” to avoid confusion with the USA.) The Americas, even in combination, are not only smaller than each of Earth’s three largest oceans (the Atlantic, Indian, and Pacific), but also smaller than Afro-Eurasia, or Eurasia — or even Asia alone, by a narrow margin.

By the way, there are lots of things that don’t show up on the second chart above: islands, inland seas, lakes, rivers, etc., and there’s a good reason for that: on the scale of even the larger pie chart above, all these things are so small, compared to the oceans and continents, that they simply aren’t large enough to be visible.

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On Binary Planets and Binary Polyhedra

Faceted Augmented Icosa

This image of binary polyhedra of unequal size was, obviously, inspired by the double dwarf planet at the center of the Pluto / Chiron system. The outer satellites also orbit Pluto and Charon’s common center of mass, or barycenter, which lies above Pluto’s surface. In the similar case of the Earth / Moon system, the barycenter stays within the interior of the larger body, the Earth.

I know of one other quasi-binary system in this solar system which involves a barycenter outside the larger body, but it isn’t one many would expect: it’s the Sun / Jupiter system. Both orbit their barycenter (or that of the whole solar system, more properly, but they are pretty much in the same place), Jupiter doing so at an average orbital radius of 5.2 AU — and the Sun doing so, staying opposite Jupiter, with an orbital radius which is slightly larger than the visible Sun itself. The Sun, therefore, orbits a point outside itself which is the gravitational center of the entire solar system.

Why don’t we notice this “wobble” in the Sun’s motion? Well, orbiting binary objects orbit their barycenters with equal orbital periods, as seen in the image above, where the orbital period of both the large, tightly-orbiting rhombicosidodecahedron, and the small, large-orbit icosahedron, is precisely eight seconds. In the case of the Sun / Jupiter system, the sun completes one complete Jupiter-induced wobble, in a tight ellipse with their barycenter at one focus, but with an orbital period of one jovian year, which is just under twelve Earth years. If the Jovian solar wobble were faster, it would be much more noticeable.

[Image credit: the picture of the orbiting polyhedra above was made with software called Stella 4d, available at this website.]

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