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Symmetry Drawing

Chapter 3: The Queen's Judgement

Having finished the symmetry checks for all the strange visitors, the judge had found that all but a few of them are at least as symmetrical as the queen. This is bad news for the judge, since the queen is eagerly waiting for his report, almost certainly sure that it was going to be in her favor.

"So, my dear judge, how did the checks go? Not as symmetrical as they claim to be, I presume?"

The judge knelt silently before the monarch, knowing that what he was going to say next was more or less guaranteed to get him thrown into the dungeons. Still, he had a job to do, and he had better see it through to the end.

"My queen," the judge replied solemnly, "I- I regret to say that the vast majority of them are... extremely symmetrical."

A moment of tense silence passed, the queen's usual poker face remaining unchanged.

Then, without so much as a warning, the tension broke.

The queen's calm facade immediately vanished, torn apart by her rage that shot up way past its boiling point. There was no civil discussion to be had, only the blind rage of the monarch, ready to pass judgement on the ones responsible for her now-inferior status.

Despite all attempts to calm the queen, there was nothing anyone in the court could do to to quell her anger and save the judge from being thrown into the dungeons.

...

.......

...........

It has been several days since I have been locked in here. Days since the fateful judging of the symmetric beings.

I did not know of their fate after I was thrown into the dungeons. Even though it was their symmetry that placed me here, I do not blame them in the slightest. After all, it is no fault of theirs that they were being punished for their mere existence. If anything, the vain queen is the only culprit here.

The dungeon food was surprisingly tasty, if you close your eyes and not think of the fact that they were essentially moldy leftovers from the castle's kitchens. Although, I suppose that probably says more about the high quality of the castle kitchens' cooking than anything. At least the queen was prideful enough to think of these as undesirable leftovers, when in reality they were feasts that the beggars and slum-dwellers of the Symmetric Kingdom would kill for.

A light chuckle escaped from my throat. The Symmetric Kingdom, what a laughably ironic name for a kingdom whose inhabitants were nearly all asymmetric.

From the corner of my eye, I spot a small hole, haphazardly covered up with rubble. Making sure no one was watching, I placed some hay under my blankets to act as a substitute, and slowly removed the rubble to open up a hole just wide enough for me to fit through, careful to place the rubble back where it belonged so as not to raise any suspicion. The hole led to a small passageway. This must have been one of the escape routes used by the previous rulers when they fled from the current queen's imprisonment.

As I crawl through the secret corridor, it eventually opened up into a wide natural cavern. My various excursions throughout the castle's surroundings led me to conclude that this cave would lead to a small community of refugees, which the queen did not know of.

Making my way out of the cave, I was greeted by a surprising, yet lovely sight. It was a small but bustling community, where both asymmetric people and the strange symmetric beings that placed me in this predicament worked and lived in peace and harmony.

I hobbled my way towards the makeshift village, barely managing to steady myself from the dungeon-induced delirium. Looking around, all I can see are perfectly symmetrical houses and perfectly symmetrical roads. The mysterious symmetric beings were numerous, of varying shapes and sizes. Instead of walking, they elegantly glided along the roads.

In fact, if it weren't for the asymmetric humans walking around, the place would seem almost eerily perfect. Lines of symmetry divided the small village into perfect mirror images of each other, and every single structure in the village that exhibited rotational symmetry had orders that are perfect multiples of four, corresponding to the four cardinal directions.

Indeed, if I had to describe this place with a single word, it would be "perfection".

As I wandered around the beautiful landscape, I spotted a familiar figure in the distance, heartily laughing with some children and some symmetric beings. Noticing my gaze, he turned towards my direction and his eyes immediately lit up with joy. Even in my delirious state, I immediately recognized him. There was no mistaking that jolly round physique and that neat symmetrical bob cut.

This person was the previous exiled king of the Symmetric Kingdom.

"Coxeter!" The former king bellowed with the trademark wide smile of his, "it has been too long, my loyal judge of symmetry! Come, let us walk!"

I let out a sigh, and made my way towards the former king. He was never one for formalities, and highly encouraged his subjects to loosen up and be more open in his presence. A good king he was, but as with any major political figure in this day and age, he also had enemies who wanted nothing better than seeing him kicked from the throne. And so, the rebels, led by the now-incumbent vain queen, staged a coup and overthrew him, ushering in a dark age of asymmetry for the once-symmetric and glorious Symmetric Kingdom.

As I walked with my former lord, I expressed my curiosity as to why he is in such a place.

"Well, you see, my boy," he guffawed, "my goal was always to build something magnificent and symmetric. A few months ago, I managed to come across a miraculous device to create symmetry. See, these beings..."

He offhandedly waved towards a symmetric being.

"These beings... They come from that device."

Immediately, my attention was piqued. Ever since my imprisonment, I had always wondered about the origins of those strange creatures.

Noticing the change in the air around myself, the former king ushered me into a tall, majestic spire, located in the center of the village.

"Come, let me show you."

Set in the middle of the interior was a strange otherworldly machine. A large screen with a grid overlain on it, doubling as a sliding door, seemed to be the centerpiece of the alien-looking device. In fact, I somehow get the impression that this door lines up perfectly with the line of symmetry that cuts the village exactly in half.

The former king went up to the device, and with a rod, he started to draw some shapes on one half of the screen. Miraculously, the other half of the screen came to life, mirroring exactly what was drawn on the king's half. As soon as he finished his drawing, he pressed a button, and a symmetric being that was shaped exactly like what was drawn emerged from the sliding screen door.

Seeing my look of utter bewilderment, the former king chuckled.

"Why don't you give it a try?"

In this simulation, you can try your hand at drawing some symmetric beings on the device. The screen is set up such that you can only draw on it by connecting the dots on the grid, but this should be sufficient for you to come up with some pretty creative shapes.

As the concept of creative limitation goes, limiting your options can boost creativity, so go ahead and create! Have fun!

Translations

Code	Language		Translator	Run

Credits

weelookang@gmail.com; Francisco Esquembre; Felix J. Garcia Clemente

Main Themes and Important Ideas:

Symmetry as a Concept: The first excerpt, through a narrative, introduces the idea of symmetry and its subjective interpretation. The "Queen's Judgement" story revolves around a vain queen who values symmetry above all else and becomes enraged when she discovers others are "at least as symmetrical as the queen." This establishes symmetry as a defining characteristic and a source of potential conflict or judgment.
Interactive Tools for Exploring Symmetry: Both excerpts point to the existence of interactive simulations (JavaScript HTML5 applets) focused on symmetry. The title of the first excerpt explicitly mentions "Symmetry Block Free Hand Only Symmetry Block Straight Line Only JavaScript HTML5 Applet Simulation Model." The second excerpt, "Symmetry Blocks Primary Math Interactives," further reinforces the availability of such interactive tools, specifically aimed at primary math education.
Practical Application through Drawing and Creation: The narrative in "The Queen's Judgement" culminates in the discovery of a "miraculous device to create symmetry." This device features a screen where drawing on one half is mirrored on the other, and upon completion, a symmetrical "being" is generated. The text explicitly invites the reader to "try your hand at drawing some symmetric beings on the device." This emphasizes the practical exploration of symmetry through creation and manipulation within the interactive environment.

Quote: "In this simulation, you can try your hand at drawing some symmetric beings on the device. The screen is set up such that you can only draw on it by connecting the dots on the grid, but this should be sufficient for you to come up with some pretty creative shapes."

Educational Applications: The context of "Open Educational Resources / Open Source Physics @ Singapore" and the title "Symmetry Blocks Primary Math Interactives" clearly indicate an educational purpose for these resources. The inclusion of "Sample Learning Goals" (though the content is "[text]") and "For Teachers" (also "[text]") suggests that these simulations are designed to support teaching and learning about symmetry.
Different Modes of Interaction: The specific mention of "Free Hand Only" and "Straight Line Only" in the title of the first excerpt's simulation suggests that different constraints and tools might be available within the interactive environment to explore symmetry in various ways.
The Role of Technology in Learning: The reliance on JavaScript HTML5 applets highlights the use of modern web technologies to deliver interactive educational content, making it potentially accessible across various devices without the need for additional plugins (compared to older Flash-based resources also listed).
Broader Context of Educational Resources: The extensive list of other simulation applets and resources on the "Open Educational Resources / Open Source Physics @ Singapore" page indicates a larger initiative focused on developing and sharing interactive tools for various science and mathematics topics. The inclusion of links to blog posts and other resources ("Version:" and "Other Resources") further supports this.
Credits and Licensing: The inclusion of translator credits and the Creative Commons license information ("Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License") in the first excerpt, along with the copyright and licensing information in the second, emphasizes the open and collaborative nature of these educational resources.

Quotes Highlighting Key Ideas:

Symmetry as a Judgment Criterion: "'So, my dear judge, how did the checks go? Not as symmetrical as they claim to be, I presume?'" (Queen speaking, demonstrating her preoccupation with symmetry).
Interactive Creation of Symmetry: "The former king went up to the device, and with a rod, he started to draw some shapes on one half of the screen. Miraculously, the other half of the screen came to life, mirroring exactly what was drawn on the king's half. As soon as he finished his drawing, he pressed a button, and a symmetric being that was shaped exactly like what was drawn emerged from the sliding screen door." (Describing the core functionality of the symmetry creation device/simulation).
Invitation to Explore: "'Why don't you give it a try?'" (The former king encouraging interactive engagement with the symmetry device).
Creative Limitation: "As the concept of creative limitation goes, limiting your options can boost creativity, so go ahead and create! Have fun!" (Justification for the grid-based drawing and potential mode restrictions in the simulation).
Target Audience: "Symmetry Blocks Primary Math Interactives" (Explicitly states the target age group and subject area).

Conclusion:

The provided excerpts introduce the concept of symmetry through an engaging narrative and highlight the availability of interactive JavaScript HTML5 applets, specifically the "Symmetry Block" simulation. These resources, part of a larger collection of open educational materials, offer a hands-on approach to learning about line symmetry through drawing and creation. The context of primary math interactives suggests these tools are designed to be accessible and engaging for younger learners. The emphasis on different drawing modes and the invitation to experiment underscore the potential for creative exploration and deeper understanding of symmetry.

The Queen's Judgement: A Study Guide

Key Concepts

Symmetry: The quality of being made up of exactly similar parts facing each other or around an axis. In the context of the story, it refers to the physical appearance and arrangement of beings and objects.
Line Symmetry: A type of symmetry where one half of an object is a mirror image of the other half across a dividing line (the line of symmetry).
Rotational Symmetry: A type of symmetry where an object looks the same after being rotated by a certain angle around a central point. The text mentions rotational symmetry with orders that are perfect multiples of four.
Asymmetry: The lack of symmetry or equality between parts or aspects of something. The majority of the "Symmetric Kingdom" inhabitants are described as asymmetric, which is ironic.
Judgement: The act of forming an opinion or evaluation by discerning and comparing. In the story, the judge is tasked with evaluating the symmetry of visitors.
Monarch/Queen: A sole and absolute ruler of a state, usually by hereditary right. The queen in the story is portrayed as vain and easily angered, particularly about her own level of symmetry.
Exiled King: A former ruler who has been forced to leave their kingdom, often due to political upheaval. The exiled king in the story sought to create a perfectly symmetrical society using a special device.
Technological Creation of Symmetry: The story introduces a device capable of generating symmetrical beings based on drawings. This highlights the distinction between naturally occurring symmetry and artificially created symmetry.
Social Commentary: The narrative subtly critiques vanity, the abuse of power, and the arbitrary nature of judgment based on superficial qualities. It also explores themes of acceptance and harmony between different groups.

Quiz

Describe the initial task given to the judge by the queen. What was the queen's expectation regarding the symmetry of the visitors?
What was the judge's surprising report to the queen, and how did the queen react to this news?
Explain the judge's feelings about the symmetric beings and the reason for his imprisonment. What does this reveal about his character?
Describe the judge's discovery in the dungeon and where the secret passageway eventually led him.
What was the most striking characteristic of the refugee community the judge encountered? Provide two specific details from the text.
Who did the judge recognize in the refugee community, and what was this person's former role?
What was the exiled king's long-term goal, and how did he claim to have achieved a significant step towards it?
Describe the function of the "miraculous device" that the exiled king showed the judge. How did it create symmetric beings?
What was the exiled king's invitation to the judge after demonstrating the symmetry-creating device? What does this suggest about the nature of the simulation mentioned in the title?
What is the irony present in the name "Symmetric Kingdom" as observed by the imprisoned judge?

Quiz Answer Key

The queen tasked the judge with checking the symmetry of all the strange visitors. The queen fully expected the judge to report that the visitors were less symmetrical than she was.
The judge regretfully informed the queen that the vast majority of the visitors were extremely symmetrical. Upon hearing this, the queen's calm facade vanished, and she became enraged, ordering the judge's imprisonment.
The judge did not blame the symmetric beings for his imprisonment, recognizing that they were being punished for their existence, not any fault of their own. This shows the judge to be fair-minded and capable of empathy.
The judge discovered a small hole hidden by rubble in his dungeon cell. This hole led to a secret passageway that was once used as an escape route by previous rulers.
The refugee community was characterized by perfect symmetry in its layout and architecture, with perfectly symmetrical houses and roads divided by lines of symmetry. Additionally, structures with rotational symmetry had orders that were multiples of four, aligning with the cardinal directions.
The judge recognized the previous exiled king of the Symmetric Kingdom in the refugee community. He was described as jolly and encouraging of openness among his subjects.
The exiled king's goal was to build something magnificent and symmetric. He claimed to have come across a "miraculous device" that allowed him to create symmetric beings.
The device had a large screen with a grid that doubled as a sliding door. Drawing a shape on one half of the screen would cause the other half to mirror the drawing, and pressing a button would result in a symmetric being emerging from the screen door.
The exiled king invited the judge to try drawing on the device himself. This suggests that the "simulation model" mentioned in the title is an interactive component allowing users to create symmetric shapes using the principles demonstrated by the king's device.
The irony is that the kingdom is named the "Symmetric Kingdom" even though the judge observes that nearly all of its original inhabitants (the ones ruled by the queen) were actually asymmetric.

Essay Format Questions

Analyze the character of the queen. What motivates her actions and how does her obsession with symmetry shape the events of the story?
Discuss the significance of the refugee community and the exiled king's actions. What commentary might the author be making about societal values and leadership?
Explore the role of technology in the story, specifically the symmetry-creating device. What are the implications of being able to artificially generate symmetry?
Examine the theme of justice and judgment in the narrative. Were the judge's actions just? Was the queen's judgment fair?
Consider the symbolism of symmetry and asymmetry in the story. What might these concepts represent in the context of the kingdom and its inhabitants?

Glossary of Key Terms

Symmetry: Correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or center.
Line Symmetry: A type of symmetry in which an object can be divided into two identical halves by a straight line.
Rotational Symmetry: A type of symmetry in which an object can be rotated around a central point by a certain angle and still look the same.
Asymmetric: Lacking symmetry.
Monarch: A sole and absolute ruler, such as a king or queen.
Exiled: Having been expelled and barred from one's native country or home, typically for political reasons.
Coup: A sudden, violent, and illegal seizure of power from a government.
Delirium: An acutely disturbed state of mind characterized by restlessness, illusions, and incoherence of thought and speech.
Cardinal Directions: The four main compass points: north, south, east, and west.
Simulation: A model or enactment of a real-world process or system, often used for study or experimentation.

App

https://play.google.com/store/apps/details?id=com.ionicframework.symmetryblock

Sample Learning Goals

[text]

For Teachers

[text]

Research

[text]

Video

[text]

Version:

Other Resources

Frequently Asked Questions about the Symmetry Block Simulation

1. What is the "Symmetry Block" simulation about?

The "Symmetry Block" simulation is an interactive tool that allows users to explore the concept of symmetry, specifically line symmetry. Users can draw shapes on one half of a grid, and the simulation will automatically mirror that drawing on the other half, creating a symmetrical figure. This tool appears to be designed for educational purposes, particularly for primary level mathematics, to help students visualize and understand symmetry through hands-on creation.

2. What is the context of "The Queen's Judgement" mentioned in the description?

"The Queen's Judgement" serves as a narrative frame for the symmetry block activity. It tells the story of a judge who finds that most visitors to the kingdom are as symmetrical as the queen, much to her displeasure. The queen's vanity and rage lead to the judge's imprisonment. This narrative provides a context for the concept of symmetry and perhaps subtly highlights the idea that symmetry can be a defining or valued characteristic within this fictional kingdom.

3. How does the simulation work?

The simulation features a grid-based interface where users can draw by connecting the dots on one side of a central line (the line of symmetry). As the user draws, the application instantly reflects the drawing across this line, creating a symmetrical counterpart. This allows for immediate visual feedback on how symmetry is formed through mirroring.

4. What is the purpose of providing both "Free Hand Only" and "Straight Line Only" options?

The description mentions "Symmetry Block Free Hand Only" and "Symmetry Block Straight Line Only," suggesting different modes within the simulation. These options likely cater to different levels of exploration or specific learning objectives. The "Straight Line Only" mode might encourage more precise drawing and a focus on how straight lines are reflected, while "Free Hand Only" might allow for more creative and less constrained exploration of symmetry. The provided embed code specifically mentions "symmetryblockstraightlineonly," indicating one of the available modes.

5. Who created the "Symmetry Block" simulation and under what license is it released?

The "Symmetry Blocks Primary Math Interactives" are credited to weelookang@gmail.com, Francisco Esquembre, and Felix J. Garcia Clemente. The compilation was done with EJS 6.0 (191124), and it is released under a specified license, although the exact license is not fully detailed in the provided excerpts. However, it is mentioned that the content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. Commercial use of the EasyJavaScriptSimulations Library requires reading their license and contacting them directly.

6. What are some potential educational applications of this simulation?

This simulation can be a valuable tool for teaching and learning about symmetry in mathematics, particularly at the primary level. It can help students:

Visually understand the concept of a line of symmetry.
Develop spatial reasoning skills by predicting how shapes will be reflected.
Engage in hands-on learning and explore symmetry in a creative way.
Understand how different types of lines (straight and freehand) can create symmetrical figures.

7. Where can this simulation be accessed and potentially embedded?

The description provides an embed code as an iframe, suggesting that the simulation can be embedded into other webpages. The src attribute of the iframe points to a specific URL: https://iwant2study.org/lookangejss/math/ejss_model_symmetryblockstraightlineonly/symmetryblockstraightlineonly_Simulation.xhtml. This indicates the web address where the "Straight Line Only" version of the symmetry block simulation is hosted and can be accessed. There is also a mention of a Google Play Store app.

8. What underlying technology is used to run this simulation?

The description explicitly mentions "JavaScript HTML5 Applet Simulation Model." This indicates that the simulation is built using web-based technologies, primarily JavaScript for the interactive functionality and HTML5 for structuring the content, likely within an applet framework for execution in web browsers. This makes it accessible across different devices without the need for specific plugins in modern browsers that support HTML5.

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Details: Written by Loo Kang Wee; Parent Category: geometry; Category: 3. Line Symmetry; Published: 19 April 2021; Created: 30 April 2018; Last Updated: 22 March 2025; Hits: 4403

Line Symmetry

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