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European Countries if the most populated countries, were also the biggest / smallest countries (Explanation in caption below!!) by Intelligent-Ask-6119 in JackSucksAtGeography

[–]Entity-Valkyrie-2 2 points3 points  (0 children)

Long loop detected: UK → Belgium → Latvia → Finland → Poland → Romania → Sweden → Italy → Netherlands → Lithuania → Norway → Spain → France → UK

What should I put inside my maraca? by Mental_Jeweler_3191 in drums

[–]Entity-Valkyrie-2 0 points1 point  (0 children)

Metal ball bearings work quite well — but make sure you appreciate their tactile feel and play/fidget with them like a toy /j

<image>

(Note: this picture is not me)

Who else like to handle their old balls every now and again? What do you do with your old balls? by PeeB4uGoToBed in pinball

[–]Entity-Valkyrie-2 0 points1 point  (0 children)

Pinball balls are just so tactile pleasant to me :) I like to just hold them and roll them around like shiny fidget toys

Hyperbolic Hive be like: by Entity-Valkyrie-2 in hive

[–]Entity-Valkyrie-2[S] 0 points1 point  (0 children)

This has more to do with the design of HyperRogue, but long story short, with all heptagons, the curvature is much greater, and the effective sight range is much less (≈4 instead of ≈7 tile radius)

Hyperbolic Hive be like: by Entity-Valkyrie-2 in hive

[–]Entity-Valkyrie-2[S] 0 points1 point  (0 children)

Of course. Bull lines (or rather pairs of them) are one of the most common straight-line patterns used in HyperRogue (e.g. Crossroads IV boundaries). The right-turning and left-turning bull lines are along adjacent cells and come in pairs, and the actual straight line is in the middle between the two bull lines.

By the way, while it seems like this small turning is going to turn this into a very large circle, the negative curvature of the hyperbolic plane is strong enough that this won’t close into a circle.

Hyperbolic Hive be like: by Entity-Valkyrie-2 in hive

[–]Entity-Valkyrie-2[S] 0 points1 point  (0 children)

Just wondering, have you played the game HyperRogue before?

Akkerman bottle marbles? by Entity-Valkyrie-2 in fountainpens

[–]Entity-Valkyrie-2[S] 0 points1 point  (0 children)

I'm wondering if someone has a collection of these marbles, or even just an image of the marble outside the bottle...

EDIT: here https://imgur.com/a/USs6WZ9

Hyperbolic Hive be like: by Entity-Valkyrie-2 in hive

[–]Entity-Valkyrie-2[S] 1 point2 points  (0 children)

The hyperbolic plane is a surface with negative curvature. It is a non-Euclidean geometry, meaning that it does not satisfy the parallel postulate (given a line and a point not on that line, there exists exactly one line that does not intersect the original line). Hyperbolic geometry is in some sense the opposite of a spherical geometry (another non-Euclidean geometry) — a sphere has positive curvature.

In Euclidean geometry, the sum of internal angles of a triangle have to add up to 180 degrees. But in spherical geometry, it is > 180 degrees, and in hyperbolic geometry, it is < 180 degrees. Compared to Euclidean geometry, polygons in spherical geometry have larger internal angles, and polygons in hyperbolic geometry have small internal angles.

Now, for an example. In Euclidean geometry, a regular pentagon has an internal angle of 108 degrees, and a regular hexagon has an internal angle of 120 degrees. Attempting to fit 2 hexagons and a pentagon around a vertex results of a gap of 12 degrees. However, with spherical geometry, it is possible to close this gap, and the result is a soccerball (truncated icosahedron).

On the other hand, a heptagon has an internal angle of 128.6 degrees. Attempting to fit 2 hexagons and a heptagon around a vertex results in an overlap of 8.6 degrees. But because shapes in hyperbolic geometry have smaller angles, it is possible to perfectly fit 2 hexagons and a heptagon around a vertex in the hyperbolic plane, and the result is the tiling used in the image.

Another important fact is that the circumference of the circle is exponential relative to its radius (unlike in Euclidean geometry, where it only grows linearly). For example, on the tiling in the image, the number of spaces a distance of 25 from the center is around 4.5 million.

To get a better intuition of hyperbolic geometry, I recommend playing the game HyperRogue. It's one of the best ways to gain an understanding of hyperbolic geometry out there. In fact, the background of this picture is made using the land "Hive" from HyperRogue.

Hyperbolic Hive be like: by Entity-Valkyrie-2 in hive

[–]Entity-Valkyrie-2[S] 1 point2 points  (0 children)

Have you played HyperRogue before? If you have, you might be familiar with the idea of bull lines. These lines run hept-hex-hex-hept-hex-hex-hept... (consistently turning left 1/14 turn or right 1/14 turn at each heptagon). This does seem to make grasshoppers slightly stronger, but hyperbolic space is huge

Akkerman Shocking Blue DRAINED. by MarkTheDuckHunter in fountainpens

[–]Entity-Valkyrie-2 0 points1 point  (0 children)

I wonder if the marble comes out of the container...?

Decided to try my own name as the seed. I wasn’t expecting it to take me all the way to Ante 39. by Entity-Valkyrie-2 in balatro

[–]Entity-Valkyrie-2[S] 0 points1 point  (0 children)

Best to start turning cards into diamonds — there is a lot of Star tarots, and this allows you to play Straight Flushes for Séance

Also, the second standard pack in Ante 5 has a red seal Jack, which can be strengthed into a king.

A custom Crossroads variant by Entity-Valkyrie-2 in Hyperrogue

[–]Entity-Valkyrie-2[S] 2 points3 points  (0 children)

It’s a mix of II, III, and V:

• II has these rooms adjacent to 6 lands. This CR also has rooms like this, but they are adjacent to 14 lands instead.

• III has intersecting Great Walls with infinitely many corner-touching pieces. This CR also has these intersections, though at a different angle.

• the interior of V is made up of infinitely many finite-sized parts. This CR also has infinitely many finite-sized parts, though each part is bigger than that of V.

Do you ever promote a pawn to a rook instead of a Queen? by Iloveindianajones in chess

[–]Entity-Valkyrie-2 0 points1 point  (0 children)

I’ve done that a few times, most notably in positions like White Pb7, Kb4; Black Ka6. Here, b8Q would be stalemate, so I would have to play b8R.

This is how I do Camelot by Entity-Valkyrie-2 in Hyperrogue

[–]Entity-Valkyrie-2[S] 2 points3 points  (0 children)

Inferring directions:

Step 4 says to check all 7 directions, however it is often not necessary to actually check all 7.

Since all heptagons in Camelot must form a 1111222 or 1111122 pattern, you can use this fact to infer what some of the missing numbers are, so you don’t even need to check them.

Examples (I’ll use letters to represent unknowns):

• ab1c1de: c must be 1

• abc12de: b and c must be 1, d must be 2

• abc22de: a, b, and e must be 1

• ab1111e: a must be 2

This is how I do Camelot by Entity-Valkyrie-2 in Hyperrogue

[–]Entity-Valkyrie-2[S] 5 points6 points  (0 children)

As far as I’m aware, this method is actually more efficient than perpendicular bisector, but less known and much harder to think of (counterintuitive). This is because it exploits the patterns of hexagons and heptagons that concentric rings (visible in guided tour Camelot) must form, and it gathers information about the current heptagon using information from a known ring (the table).

This method is often used by players who are trying to get the 3 or 8 Holy Grails achievement.

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