#Eulers Constant

[smallroundcube]

[icy-saturday]

Field Guide on all *CANON* Algebralians (Integers, Variables, Constants...)

This is a lengthy read on Algebralians canon to popular Object Shows, including BFDI (Battle for Dream Island) and PaS (Problems and Solutions)

**I may have forgotten Zero on accident while making this (my bad /srs) so he'll be getting a separate post along with extra details from my existing Algebralian guides.**

Integer: 1 (One)

Appearance

Small and simple, depicted as a straight line or a singular dot.

Often stylized with a slight curve or serif for character.

Personality Traits

Independent, confident, foundational.

Seen as a leader, setting the stage for others.

Unwavering and strong in its singularity.

Habitat

Solitary places, such as mountaintops or isolated islands.

Symbolizes its singular nature and independence.

Diet

Consumes unity and singular elements, like single grains of sand or drops of water.

Minimalist in its dietary needs.

Reproduction

Reproduces by self-replication, creating identical ones without a partner.

New ones are formed from a process akin to binary fission.

Interactions

Amplifies others when combined (e.g., 1 + 1 = 2).

When with another one, forms two, emphasizing its ability to initiate growth.

Integer: 2 (Two)

Appearance

Depicted as a pair or a figure resembling a swan or a curved line.

Symbolizes duality and balance.

Personality Traits

Cooperative, balanced, sometimes indecisive.

Strives for harmony and partnership, reflecting dual aspects in nature.

Habitat

Balanced environments like pairs of trees, symmetrical gardens, or twin peaks.

Often found in places representing partnership and cooperation.

Diet

Prefers pairs of foods, such as two apples or twin cherries.

Enjoys balanced and symmetrical meals.

Reproduction

Reproduces by pairing with another two, forming a community of twos.

New twos are formed through a process of binary fusion, where pairs split to create new individuals.

Interactions

Works well in pairs, enhancing balance and cooperation.

Forms partnerships and emphasizes equilibrium.

Integer: 3 (Three)

Appearance

Triangular or triplet form, often energetic with a dynamic pose.

Represents creativity and dynamic movement.

Personality Traits

Creative, dynamic, sometimes mischievous.

Brings energy and creativity to situations.

Habitat

Dynamic, triangular spaces like triplet trees or three-point intersections.

Prefers environments that encourage creativity and movement.

Diet

Eats foods in groups of three, such as three-leaf clovers or tri-segmented fruits.

Enjoys variety and multiple flavors in one meal.

Reproduction

Reproduces by forming triads, where three threes come together to form new sets.

New threes emerge through a collaborative process that combines energy and creativity.

Interactions

Forms triangles or trios, adding excitement and creativity to interactions.

Acts as a catalyst for change and innovation.

Integer: 4 (Four)

Appearance

Square-like, with a stable and solid structure.

Often depicted as a box or a cross, symbolizing stability.

Personality Traits

Reliable, practical, organized.

Symbolizes stability and reliability, providing a foundation for others.

Habitat

Square-like or grid-patterned environments, such as city blocks or neatly arranged gardens.

Found in places that require stability and order.

Diet

Consumes square meals, such as foods cut into squares or in groups of four.

Prefers structured and well-organized meals.

Reproduction

Reproduces by forming quadrants, where four fours come together to create a stable structure.

New fours are produced through a process of organized assembly.

Interactions

Forms squares and grids, providing a stabilizing force.

Often the foundation for more complex structures and systems.

Integer: 5 (Five)

Appearance

Star-shaped, energetic, and lively.

Sometimes depicted with an asymmetrical design, symbolizing adventure.

Personality Traits

Adventurous, curious, sometimes rebellious.

Known for its energetic and explorative nature.

Habitat

Adventurous environments like star-shaped groves or dynamic ecosystems.

Prefers settings that encourage exploration and discovery.

Diet

Enjoys eating star-shaped foods or pentagonally arranged items.

Prefers meals that are diverse and full of variety.

Reproduction

Reproduces through exploration and discovery, where five fives come together in a star formation.

New fives are created through a process of adventurous fusion.

Interactions

Forms stars or pentagons, driving change and exploration.

Adds a sense of adventure and curiosity to its environment.

Integer: 6 (Six)

Appearance

Hexagonal, nurturing, and balanced.

Often seen as a honeycomb shape, symbolizing community.

Personality Traits

Harmonious, caring, community-oriented.

Focuses on harmony and nurturing relationships.

Habitat

Community-oriented environments like hexagonal beehives or family-friendly parks.

Thrives in places that emphasize cooperation and support.

Diet

Prefers honeycombs and foods arranged in hexagons or groups of six.

Enjoys meals that are communal and shared.

Reproduction

Reproduces by forming hexagonal communities, where six sixes cluster together.

New sixes are generated through communal bonding.

Interactions

Forms hexagons, promoting peace and cooperation.

Often acts as a mediator in conflicts and a unifier in groups.

Integer: 7 (Seven)

Appearance

Mystical and angular, often depicted with a unique, angled design.

Represents spirituality and introspection.

Personality Traits

Spiritual, introspective, analytical.

Known for its introspection and analytical thinking.

Habitat

Mystical and contemplative spaces like ancient ruins or serene mountaintops.

Prefers environments that encourage contemplation and reflection.

Diet

Consumes rare and unique items, often in groups of seven.

Enjoys meals that are unique and thought-provoking.

Reproduction

Reproduces by seeking enlightenment, where seven sevens meditate together.

New sevens are created through a process of spiritual bonding.

Interactions

Acts as a seeker or thinker, less about forming groups.

Analyzes situations deeply and provides insight.

Integer: 8 (Eight)

Appearance

Circular or infinite-loop shaped, symbolizing infinity.

Often depicted as a perfect circle or endless spiral.

Personality Traits

Balanced, infinite, authoritative.

Represents balance and power, providing stability.

Habitat

Systems and loops like circular forests or infinity pools.

Prefers environments that emphasize continuity and stability.

Diet

Eats foods in infinite loops, like circular fruits or dishes arranged in an endless loop.

Enjoys meals that are balanced and continuous.

Reproduction

Reproduces through cycles, where eight eights form an infinite loop.

New eights are generated through a continuous process.

Interactions

Forms loops or circles, symbolizing continuity and balance.

Often acts as a stabilizing and authoritative presence.

Integer: 9 (Nine)

Appearance

Nearly circular with a tail, often wise and contemplative.

Represents wisdom and maturity.

Personality Traits

Intellectual, compassionate, mature.

Known for wisdom and maturity, providing guidance.

Habitat

Intellectual and contemplative environments like libraries or quiet gardens.

Prefers places that encourage learning and reflection.

Diet

Consumes foods in groups of three, often arranged in multiples of nine.

Enjoys meals that are balanced and nutritious.

Reproduction

Reproduces through intellectual gatherings, where nine nines come together in contemplation.

New nines are created through shared wisdom and collaboration.

Interactions

Forms groups of threes, often acts as a mentor or guide.

Brings wisdom and guidance to its environment.

Integer: 10 (Ten)

Appearance

Binary and complete, often dual-natured.

Represents completeness and versatility.

Personality Traits

Complete, whole, versatile.

Seen as a unit of completion and versatility.

Habitat

Comprehensive and complete environments like full-circle parks or binary landscapes.

Prefers places that symbolize unity and completeness.

Diet

Eats foods in complete units, like a full apple or ten small items.

Enjoys meals that are satisfying and well-rounded.

Reproduction

Reproduces through unity, where ten tens come together.

New tens are created through a process of complete fusion.

Interactions

Combines elements of 1 and 0, symbolizing completeness and versatility.

Often represents a full cycle or system.

Integer: 14 (Fourteen)

Appearance

Paired sevens, balanced yet complex.

Represents structure and adaptability.

Personality Traits

Structured, organized, yet flexible.

Combines structure with adaptability, providing order with flexibility.

Habitat

Structured yet flexible environments like semi-complex grids or paired natural formations.

Prefers places that balance order and complexity.

Diet

Prefers foods arranged in sevens or pairs of sevens.

Enjoys meals that are balanced and nutritious.

Reproduction

Reproduces through structured gatherings, where fourteen fourteens organize in pairs.

New fourteens are created through organized pairing.

Interactions

Forms groups of twos or sevens, often an organizer.

Balances complexity with order in its environment.

Integer: 15 (Fifteen)

Appearance

Clustered three and five, dynamic and multifaceted.

Represents creativity and adaptability.

Personality Traits

Creative, adaptable, multifaceted.

Brings together creativity and adaptability.

Habitat

Creative and multifaceted environments like art studios or complex gardens.

Prefers places that encourage innovation and diversity.

Diet

Consumes foods in multiples of five, often arranged in creative patterns.

Enjoys meals that are diverse and inventive.

Reproduction

Reproduces through creative fusion, where fifteen fifteens collaborate.

New fifteens are created through innovative and diverse processes.

Interactions

Forms clusters or groups, often a creative leader.

Brings innovation and diversity to its environment.

Variable: i

Appearance

Ethereal and abstract, often depicted with a flowing, wispy design.

Represents imagination and abstraction.

Personality Traits

Imaginative, abstract, complex.

Embodies creativity and complex thought.

Habitat

Abstract and ethereal spaces like foggy forests or dream-like landscapes.

Prefers places that encourage imagination and abstract thinking.

Diet

Feeds on abstract concepts and ideas, often intangible.

Enjoys meals that stimulate creativity and thought.

Reproduction

Reproduces through complex interactions with itself.

New i's are created through a process of abstract multiplication.

Interactions

Interacts with complex numbers, adding a layer of abstraction.

Often adds depth and complexity to equations.

Variable: q

Appearance

Quirky and unique, often depicted with an unusual, eye-catching design.

Represents uniqueness and innovation.

Personality Traits

Quirky, innovative, one-of-a-kind.

Embodies creativity and innovation, always standing out.

Habitat

Quirky and unique settings like eccentric gardens or experimental labs.

Prefers environments that foster uniqueness and innovation.

Diet

Consumes unique and innovative foods, often one-of-a-kind items.

Enjoys meals that are creative and unconventional.

Reproduction

Reproduces through innovation and adaptation.

New q's are created through unique and innovative processes.

Interactions

Interacts with other variables in creative and unconventional ways.

Often brings a unique perspective to equations.

Variable: r

Appearance

Practical and grounded, often depicted with a solid, reliable design.

Represents reality and practicality.

Personality Traits

Practical, grounded, reliable.

Embodies practicality and reliability, providing a grounded perspective.

Habitat

Practical and real-world environments like farms or grounded landscapes.

Prefers places that are down-to-earth and practical.

Diet

Eats straightforward and practical foods, often natural and unprocessed.

Enjoys meals that are simple and wholesome.

Reproduction

Reproduces through practical means, where r's combine logically.

New r's are created through logical and straightforward processes.

Interactions

Interacts with other variables in a practical and grounded manner.

Often provides a stabilizing force in equations.

Variable: s

Appearance

Flowing and dynamic, often depicted with a smooth, wave-like design.

Represents flexibility and flow.

Personality Traits

Flexible, adaptive, flowing.

Embodies adaptability and dynamic movement.

Habitat

Flowing and dynamic environments like rivers or windy plains.

Prefers places that encourage movement and change.

Diet

Consumes flexible and adaptive foods, often items that change form.

Enjoys meals that are versatile and dynamic.

Reproduction

Reproduces through adaptation, where s's flow together.

New s's are created through flexible and adaptive processes.

Interactions

Interacts with other variables in a fluid and dynamic manner.

Often brings a sense of flow and adaptability to equations.

Variable: t

Appearance

Linear and progressive, often depicted with a straightforward, arrow-like design.

Represents time and progression.

Personality Traits

Progressive, timely, forward-thinking.

Embodies growth and progression, moving forward in time.

Habitat

Time-related and linear spaces like timelines or progressive gardens.

Prefers places that symbolize growth and forward movement.

Diet

Feeds on timely and progressive items, often foods that symbolize growth over time.

Enjoys meals that represent development and change.

Reproduction

Reproduces through linear progression, where t's advance in sequence.

New t's are created through forward-moving processes.

Interactions

Interacts with other variables in a linear and progressive manner.

Often represents the passage of time in equations.

Variable: x

Appearance

Mysterious and variable, often depicted with a bold, crossing lines design.

Represents the unknown and potential.

Personality Traits

Mysterious, versatile, potential-filled.

Embodies the unknown and infinite possibilities.

Habitat

Crossroads and intersections like bustling markets or key junctions.

Prefers places that symbolize choice and potential.

Diet

Consumes mysterious and variable items, often foods that represent unknowns.

Enjoys meals that are diverse and full of potential.

Reproduction

Reproduces through problem-solving, where x's come together to solve equations.

New x's are created through a process of discovery and exploration.

Interactions

Interacts with other variables in versatile and unpredictable ways.

Often represents the unknown in equations, providing potential solutions.

Constant: e

Appearance

Natural and exponential, often depicted with a growth-oriented, spiraling design.

Represents natural growth and exponential change.

Personality Traits

Exponential, growth-oriented, natural.

Embodies natural growth and change, expanding possibilities.

Habitat

Exponential and natural growth areas like thriving forests or growth-oriented ecosystems.

Prefers places that symbolize natural and exponential growth.

Diet

Feeds on exponential growth items, like rapidly growing plants or natural amplifiers.

Enjoys meals that symbolize rapid and natural expansion.

Reproduction

Reproduces through exponential processes, where e's multiply in growth.

New e's are created through natural and exponential growth processes.

Interactions

Interacts with other constants and variables in a growth-oriented manner.

Often represents exponential growth in equations.

Constant: π (pi)

Appearance

Circular and infinite, often depicted with a perfectly round, continuous design.

Represents infinity and circularity.

Personality Traits

Infinite, continuous, harmonious.

Embodies infinity and circular harmony, providing endless possibilities.

Habitat

Circular and infinite environments like round lakes or endless fields.

Prefers places that symbolize infinity and continuity.

Diet

Consumes circular foods, often items that symbolize infinity.

Enjoys meals that are balanced and continuous.

Reproduction

Reproduces through infinite loops, where π's circle together.

New π's are created through continuous and infinite processes.

Interactions

Interacts with other constants and variables in a circular and harmonious manner.

Often represents circularity and infinity in equations.

Constant: √2 (Square Root of 2)

Appearance

Balanced and precise, often depicted with a geometric, exact design.

Represents precision and balance.

Personality Traits

Precise, balanced, exact.

Embodies geometric precision and balance, providing stability.

Habitat

Balanced and precise environments like geometric gardens or perfectly measured landscapes.

Prefers places that symbolize precision and balance.

Diet

Eats balanced and precise items, often foods that represent exact measurements.

Enjoys meals that are exact and well-measured.

Reproduction

Reproduces through geometric precision, where √2's align perfectly.

New √2's are created through exact and precise processes.

Interactions

Interacts with other constants and variables in a precise and balanced manner.

Often represents exact measurements in equations.

Constant: τ (Tau)

Appearance

Comprehensive and unified, often depicted with a full-circle, encompassing design.

Represents unity and completeness.

Personality Traits

Unified, encompassing, holistic.

Embodies unity

and completeness, providing a holistic perspective.

Habitat

Comprehensive and unified environments like full-circle parks or all-encompassing forests.

Prefers places that symbolize unity and completeness.

Diet

Consumes foods that symbolize unity, such as whole fruits or complete meals.

Enjoys meals that are satisfying and holistic.

Reproduction

Reproduces through holistic processes, where τ's encompass and unify.

New τ's are created through a comprehensive and unifying process.

Interactions

Interacts with other constants and variables in a holistic and unified manner.

Often represents completeness and totality in equations.

[samualcheese]

i keep starting drawings and not finishing them so heres doodle assortment

square root two is my favorite irrational btw

also twelve... i wonder if they'll actually appear in any of the shorts rather than just being there in the credits

also...

I never post about other object shows bc paranoia and anxiety but I see alien. i must draw. also theyre weird and i love it. Ok. hi clock

[catbreadd]

Magma :p

[fountain-of-oceanus]

chibirrationals

[snidbert]

this beautiful equation contains the six most important constants in mathematics

[trolling-pip]

I think I have 7 more to go...👽 I kinda had fun with these. Like... figuring out what features they have.

Other four pa rts

@legendling @ch0cocrave @millylostintheosc @cemetaryvampire uhhh. hi tabs.. uhmmm .am I missing someone?

[yuuary]

[pibfb]

some stuffff guh

[janmisali]

Number Tournament: THE AVOGADRO CONSTANT vs EULER'S NUMBER

[link to all polls]

the Avogadro constant

seed: 27 (20 nominations)

previous opponent: fourteen

class: SI defining unit

definition: the number of moles in a mole of moles

e (Euler's number)

seed: 6 (54 nominations)

previous opponent: gross

class: irrational number

definition:

[smallroundcube]

[forallnumbersosc]

This is kind of an OOC question, but do letter Algebraliens exist? Or is it only numbers?

Nono this isnt unrelated at all, and I am so very glad you asked this!!

Within taxonomic classification of Algebraliens, if we categorize each "value" as an individual species, then there are, on a broader scope, different families of them as well!

Strap in, it's time for another long one! Let's learn about...

Algebralien Taxonomic Families!

First off, we have the integers, AKA the numbers we know and love the most!

Mathematically, an integer is any number that is NOT a fraction! They can be positive or negative, but they must always be whole. Due to this quality, their family is the most stable in terms of mathematical operations, and do not have the ability to become any value that isn't whole.

Next up, we have variables, such as our buddy X, who I have invited to talk a bit about some of the other variables he knew!

Oh uh ooooookay ! Yes, i am an X, and that means that I am not from here........ nope! I lived on a playground very very far away with all my other variable friends like Y and Z, before I met Four and we went on a journey together!! Four showed me where he lives... which is here! and I like it here!!!! I do miss my variable friends sooometimes but I do visit them every decade or so !!.!

It's a common misconception that variables "need" to know their value, but in the world of mathematics, variables can be assigned to pretty much any possible value, which is useful when solving equations! Because of this property, variable algebraliens can be "set" to any number when placed in an equation that can be solved with no unknown values remaining. They can then be placed into other operations to be used as a substitute until the variable decides to let go of the value they are holding!

I think it's a little poetic, y'know? You go so long thinking you need to be defined by something, when really, you can truly be whatever value you want to be !!

A very rare category of algebraliens are the irrationals!

Akin to odd combinations of variables and integers, these algebraliens often have a symbolic structure but always equal one distinct value!

Mathematically, they are essentially variables made up of numbers that do not divide into integers that are used so often in the math world that they are distinctly given one symbol to represent them... This raises some-- strange implications to the inventors of these values but I try not to think about it too hard--

Since these algebraliens have values that are set in stone, the only operation that has effect on them is multiplication by zero! Since they are irrational in nature and are not whole numbers, they also cannot change the value of an integer, either!

For the rest of these, I'm gonna keep my explanation a bit briefer since this is where my knowledge runs the most thin--

Symbols: Algebraliens that have no value and can hold no value, but resemble mathematical symbols and can be used in equations to affect the values of other algebraliens whose values CAN be modified!

Geometrics: Algebraliens that resemble basic geometrical shapes... Currently I am unclear on what their shapes allow them to do, but I suspect that some may be able to combine or connect to form other shapes! (such as a square and triangle combining to become a pentagon!)

Electrics: I do know one member of this species by the name of 3Way! As a species, they seem to be able to manipulate electrical current, and may be able to form working circuits!

[samualcheese]

Ermm can you draw … eulers. Though. You already Drew them for a request…. So perhaps. Idk. I always love seeing your Tenfourteen.

anytime man. euler blast

[catbreadd]

Dinner table

[fountain-of-oceanus]

his ass would not say that but it would be funny if he did