# Welcome to PolygonTrix™

PolygonTrix is a Math Art Game, a digital arcade of angles and energy that lets you explore the space-time dynamics hidden inside polygons!

To you, the display may LOOK like a pool ball game, but PolygonTrix IS NOT a shooting game — it's an amusing geometric puzzler with a particle physics twist.

PolygonTrix can be played solo, or by parent & child, or by any two players who agree to share particles.

# Getting Started

Polygons have vertices & sides. Particles have energy levels, direction, and location.

The game opens with a particle loaded in the chamber. The particle will be charged with ONE unit of energy. Additional uncharged particles are waiting in the magazine.

Touch the charged particle — it will pop into the polygon. A target will appear at the first vertex.

Rotate the particle toward the target using the compass control, or move it using a dragging gesture. (There's more about controlling the particle below.)

In the simple warm-up round, the path will be straight in to the target. The path will light up when it is lined up with the target. When the path lights up, lift your finger, and the target will change into a black hole!

The polygon warm-up round proceeds until the particle magazine is empty.

Now PolygonTrix gets tricky. Why?

No target can accept a particle with more than a single unit of charge.
But, on the higher energy levels of the game, the particle is charged with multiple energy units! So deflective force must be used to reduce the particle's charge so it may enter the target, completing its event so the game can continue.

# Playing the Game

Each round begins with the particle magazine loaded with particles, one for each vertex of the polygon. One particle will be loaded in the chamber and charged with energy.

After the warm-up round for the polygon, the particle is charged with multiple units of energy. The energy level is increased as each round is completed.

You touch the charged particle to pop it into play inside the polygon at a random location, pointed in a random direction. The future path of the particle is always traced out at the speed of light.

#### Targets

Targets appear only at polygon vertices.

As we saw in the warm-up round, when the World Line transects the target and the particle is released, the target changes to a black hole. The black hole remains in the polygon until the round is completed, making the remaining conversions a little more challenging.

Once a target is converted, you'll see your new total score.

#### Particle Direction (Rotating the Particle)

You control the direction of the particle with the compass:

• The Outer Dial controls +/- degrees.
• The Inner Dial controls +/- minutes. 1 minute = 1/60th of 1°.
• You can use any portion of either dial like a steering wheel.
• You only need to touch within one of the dials to start, then you can wind around the particle any way you like to turn it.

#### Particle Location (Moving the Particle)

You can move the particle around inside the polygon. Place your finger on the particle, then move it. [See Laws below.] The particle retains its direction while being moved.

#### Particle Deflections and Rejections

A Black Hole always rejects particles. In this game, nothing can enter or interact with a black hole.

A target may reject a particle. The particle's energy must be reduced to unity (one unit) by deflections before reaching the target in order to interact with it. Each deflection takes one unit of charge from the particle. Trix does the arithmetic. All you have to do is play!

Your challenge is to find a World Line (path) connecting the particle to the target while using all the deflections to properly discharge the particle.

The World Line shows a rejection by changing color.

#### The World Line

Trix always displays the entangled path or "World Line" of the particle. The World Line ends at the target, or at a black hole, or it dead-ends on a side of the polygon.

Trix instantaneously shows the World Line for the particle as it is rotated or moved. The World Line turns orange if it reaches a black hole. This is called rejection. [See Deflections and Rejections above.] The World Line also turns orange if it reaches the target "too soon", before the particle is properly discharged. The World Line is your view into the future.

The World Line widens if the target accepts it. Lift your finger, and you'll see a flux of hundreds of future arcs along the World Line.

#### Energy Levels

The Energy Level Indicator shows the number of deflections the particle will make before a single charge remains. The ELI is a miniature representation of the World Line you see inside the polygon during PARTICLE IN PLAY.

#### Flux

When a Target is converted to a black hole, a geometric pattern is made by extending the World Line through 512 deflections. This geodesic flux is unaffected by any black holes that may have been formed in the polygon.

If the resulting flux seems to have only a few lines, think about what you are seeing. Read about orbits in the FAQ on our website.

There is a switch in Settings for showing the flux while the particle is in play. The Playing Flux is an extension of the World Line through 128 deflections.

#### Playing the Whole Game

• You can switch directly to a polygon with three to nine sides at any time.
• Each of the seven polygons is a separate game with 11 levels to unlock.
• For any polygon, you proceed by levels.
• As you complete each level, the polygon automatically "levels up" — the number of units of energy charge increases, and you get a new supply of uncharged particles.
• If any particles are remaining in the magazine, a new particle is charged. Touch it to play.
• When the particle magazine is empty, all the targets will have been converted, completing the level, so the next level is unlocked for play, and the magazine is automatically reloaded.
• The difficulty increases with the number of deflections, especially on odd-sided polygons.
• Once all 11 energy levels are complete, the polygon is done.
• Once all polygons are done, the game is over.
• You can reset any polygon or the Whole Game by using the Settings tab. Be Careful!

Each polygon presents a unique space-time challenge. You can just be a "Banger" and toy around, or you can use your wits to become a PolygonTrix Master.

# What Counts?

Warm-ups don't count, but must be played.

The score is the total number of sides hit while converting the targets on all levels of all polygons, so it's to your advantage to employ as many sides as you can in each conversion event.

By "as many sides as you can", we mean effectively using the number of deflections happening in the energy level. For example: The World Line can't possibly reach all 8 sides of the octagon when the octagon is on Energy Level 3, because level 3 has only two deflections — there can be only 2 counts. Another example: On energy Level 7, you could waste counts by just using 2 of the six sides on a square or hexagon, and so on. See Tips for advice on using the deflection detectors.

Most of the points are on the higher energy levels of the larger polygons, but in order to get the highest possible game score, you must score perfectly across all polygons.

There are 11 levels x (3+4+5+6+7+8+9) vertices = 462 conversion events. The maximum score obtainable is 1,932!

You can change to a different polygon at any time without losing the counts on the current polygon. The states of all polygons are saved when Trix quits.

# Laws

For safety reasons, you cannot move the particle itself near any vertex. (You have to stay out of the polygon's "corners".) Moving the particle causes the polygon's incircle to appear as a warning.

The Law of Deflection: The angle of deflection equals angle of incidence. These computations are handled by PolygonTrix.

# Settings (Resetting the Whole Game or just a Polygon)

You can reset the whole game. The RESET PolygonTrix button on the Settings tab resets all vertices on all levels on all polygons. Each polygon will again require the warm-up round. The reset operation cannot be undone.

You can reset just a particular polygon by tapping the corresponding button on the Settings tab. Resetting a polygon re-locks all its levels. The polygon will also require the warm-up round. A polygon reset cannot be undone.

We suggest resetting a polygon early in the game just to see how that works. Or not.

An ON/OFF switch enables a Playing Flux during PARTICLE IN PLAY. It's fun just to play with the flux. Don't forget the target!

# Tips

You can tap the compass on either side of the World Line to tweak the direction by one degree or minute. When you acquire the target with a single tap, you will need to tap one more time to actually convert it.

The polygon sides have deflection detectors. To score the maximun count for a given conversion, use as many different sides as you can. Check the detectors to see if one side is un-visited, that no other side is visited twice. Remember — the event doesn't happen till you lift your finger.

Each unplayed polygon shows how a particle could continuously deflect in an "orbit".

Be sure to scan Trix's FAQ on our website for background information and updates.

There is a slight chance that the particle's intial random location and direction will form a World Line that transects the target. Don't be surprised if you see that happen! You can just make the conversion by slightly moving or rotating the particle. Or you can turn or move the particle away to avoid the conversion (and that "particular" fate for the particle).

You'll see how even-sided tables can be trivial, because you can just make the World Line go back and forth between a pair of parallel sides at a shallow angle, and zig zag on in to the target. To make the game more interesting, you get a "count" for each unique side involved in your shot.

# The Future of PolygonTrix

The next version of PolygonTrix will have a Game Center leader board. Points you earn with this version should be retained for later versions, unless you reset a polygon or the game.

We may animate particle events and make sounds for entertainment in an a futre version of PolygonTrix. (Even an App has a World Line in iSpace.)

# Please Check Out Our Other Apps!

The Polygon is an archetypal form, and reflections are a dynamic physical reality. As with our Geom-e-Tree App, PolygonFlux lets you explore a form like never before.

PolygonFlux is based on "Polygonal Billiards", an active area of geometric research. We hope it will be used by teachers to demonstrate, and by students to explore.

PolygonFlux can be used just for fun to explore the esthetic variation of patterns created by lines, colors, and shadows.

Visit polygonflux.com.

The Tree is also an archetypal form. Geom-e-Tree lets you explore this form via multi-touch gestures. You just need to be curious, visual, creative, or meditative - and ready for some unpredictable results. Geom-e-Tree will also hold intellectual appeal for mathematicians and scientists, artists and designers, educators and students.

Visit Geom-e-Tree.com.

# A Challenge for Other Developers

PolygonTrix ©2012, by John Miller, Portland, Oregon, USA. This app will have other features added in later versions. We really don't want to see copycat variants of our basic design. We ask other developers to respect our right to improve PolygonTrix, and challenge them to come up with their own creative ideas to enrich the electronic playground and classroom. Thanks!

Build 1.2 December 10th, 2012.