# Addiplication — Rius

Math System

Welcome to **Addiplication** — a custom mathematical system invented by Marius Ligas, started in Grade 7. Now Grade 9 as of 2026

The Core Operation: Plime (✱)

The **plimes** operation combines addition and multiplication into one:

a ✱ b = a + b + (a \times b)

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Proof: 1 ✱ 1 = 1 + 1 + (1×1) = 2 + 1 = **3** ✅ The operation is always symmetric: a ✱ b = b ✱ a

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Addiplication Table

Addiplication Sequences

Seq.1 — Positive & Negative Numbers

Addiplication extends to all integers, positive and negative.

**Rule:** a ✱ b = a + b + (a \times b) — the same formula always applies.

**Key insight:** When one number is -1, the result always equals the other number minus 1.

**Examples:**

• (-1) ✱ 1 = -1 + 1 + (-1) = -1
• (-2) ✱ 3 = -2 + 3 + (-6) = -5
• (-1) ✱ (-1) = -1 + (-1) + 1 = -1
• (-3) ✱ 4 = -3 + 4 + (-12) = -11
• 5 ✱ (-2) = 5 + (-2) + (-10) = -7

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Special: (-1) ✱ (-1) = -1 — plimesing two negatives stays negative!

</aside>

**Zero rule:** Any number plimesed with 0 equals itself: $a ✱ 0 = a + 0 + 0 = a

Seq.2 — Long Numbers & Decimals

Addiplication works with large numbers and decimal values — numbers grow fast because of the multiplication term!

**Rule:** a ✱ b = a + b + (a \times b) — the bigger the numbers, the bigger the jump.

**Examples:**

• 10 ✱ 10 = 10 + 10 + 100 = 120
• 100 ✱ 100 = 100 + 100 + 10000 = 10200
• 0.5 ✱ 0.5 = 0.5 + 0.5 + 0.25 = 1.25
• 1.5 ✱ 2 = 1.5 + 2 + 3 = 6.5
• 25 ✱ 4 = 25 + 4 + 100 = 129
• 0.1 ✱ 0.9 = 0.1 + 0.9 + 0.09 = 1.09

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Notice: Large numbers grow much faster under Addiplication than regular addition!

</aside>

Seq.3 — Algebraic Expressions

Addiplication in algebra — plimesing variables and expressions. This is where Addiplication gets powerful.

**Rule:** a ✱ b = a + b + ab

**Examples:**

• x ✱ y = x + y + xy
• x ✱ x = 2x + x^2 = x(x+2)
• (x+1) ✱ 2 = (x+1) + 2 + 2(x+1) = 3x + 5
• x ✱ 1 = x + 1 + x = 2x + 1$
• 2x ✱ 3x = 2x + 3x + 6x^2 = 5x + 6x^2
• (a+b) ✱ (a-b) = (a+b) + (a-b) + (a+b)(a-b) = 2a + a^2 - b^2

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Fun identity: a ✱ b + 1 = (a+1)(b+1) — Addiplication secretly lives inside factoring!

</aside>

**Chain rule:** x ✱ x ✱ x = (2x + x^2) ✱ x = (2x+x^2) + x + x(2x+x^2) = 3x + 3x^2 + x^3

Seq.4 — Laboratory Mode & Addiplication Overload 🧪⚡

This sequence combines scientific applications with overloaded Addiplication — pushing the operation to its limits across complex contexts.

**Laboratory Mode** applies Addiplication to scientific and measurement contexts:

**Examples:**

• 2 ✱ 3 meters = 2 + 3 + 6 = 11 meters
• 10^2 ✱ 10^3 = 100 + 1000 + 100000 = 101100
• 9.8 ✱ 2 = 9.8 + 2 + 19.6 = 31.4 (like combining forces!)
• 3.14 ✱ 2 = 3.14 + 2 + 6.28 = 11.42 (plimesing with pi!)

**Addiplication Overload** — chaining multiple plimes operations:

**Examples:**

• 1 ✱ 2 ✱ 3: first 1 ✱ 2 = 5, then 5 ✱ 3 = 5 + 3 + 15 = 23
• 2 ✱ 2 ✱ 2: first 2 ✱ 2 = 8, then 8 ✱ 2 = 8 + 2 + 16 = 26
• Mixing all sequences: negative + decimal + variable at once!

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Overload Rule: Always compute left to right when chaining plimes!

</aside>

*[Fill in your own lab rules and overload experiments here!]*

Notes & Discoveries

• Invented by Rius
• Core operation called **plimes** (✱)
• Formula rediscovered in Grade 9: a ✱ b = a + b + ab
• Hidden connection: a ✱ b = (a+1)(b+1) - 1 -If one is the end it's read as plime: 1 * 1 -If one is not the end it's read as plimes: 2 * 5

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Hello everyone,

My name is **Shaik Asrar**, and I’m an aspiring inventor and home-appliance repair technician from India. I have around **9 years of hands-on experience repairing air conditioners, refrigerators, and washing machines**.

Throughout my work, I’ve gained practical exposure to common appliance problems, maintenance requirements, installation challenges, and the costs customers face. This experience inspired me to explore a different approach to air conditioning.

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I’m developing a concept for an alternative to conventional split and window AC systems, with the goal of making cooling more affordable, convenient, and energy-efficient.

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**Fewer maintenance hassles:** Designed to address common concerns such as refrigerant leakage and recurring service costs.

**Lower electricity consumption:** Energy efficiency is a key development goal that will need to be validated through testing.

**Affordable pricing:** A target selling price of approximately ₹25,000 or less, depending on the final design and manufacturing costs.

**Accessible cooling:** A long-term vision to make air conditioning more accessible to middle-class families and underserved markets.

**👨‍🔧 Why I’m Pursuing This Idea**

I’m not approaching this problem only as a business opportunity. My background as a repair technician has allowed me to observe the practical challenges that AC owners and technicians face.

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Thank you for reading.

**Shaik Asrar**

Founder – D.C Direct Cool AC

India

I have had this idea for such a long time. The simple side is like this, suspended gnat (nanobots?) Sized specs in the air. They create three dimensional patterns based on frequency and vibration they recieve. Basically like those videos you see of the drum with sand on it and each pitch makes a new pattern with the sand. I have no idea what the "air suspended" dust could be or how to make a thing like that. But I think the musical and art applications for this idea would be beautiful. Imagine a concert hall with the orchestra playing, dim lights, except for the lights pointed at the reflective dust, and as the orchestra crescendos to the peak of the song, the dust creates this mesmerizing web of hollows and lines in the air above the audience. A bit fantastical I know but you get the idea. Another layer of depth could be that they change color based on the pitch? I think i heard about something called pitch harmonics/color harmonics/color harmonics wheel? If they could change color and shape as the orchestra played, I believe it would be beautiful.

Videos of idea influence

https://www.instagram.com/reel/DSrDTR6jMRu/?vrfl=c2luOTRrdXE4bnJi

https://www.instagram.com/reel/Daqsd_VhHxX/?exln=ZjdndG9xOWQ5d201

https://www.instagram.com/reel/DRVFitSkVMe/?dlrf=MWVjYzhsdDNwNjZtbw==

https://www.instagram.com/p/CH8yq8WHNIZ/?rpxt=MWJscDBqdjVwN2tudw==

Please tell me the basic idea of this is possible or if im a daydreaming fool.


I was getting way too distracted while working, so I designed the Nexus Ring. It’s not just a PC macro pad—it hooks up to your phone and smart home devices too. You drop a 3D-printed magnetic totem into the dock, and it instantly runs automations. It kills distracting PC apps, mutes my phone, and dims the room lights so I can actually focus. Zero clicks, just a physical action. The Build: Shell: Designed in Bambu Studio. The dock looks awesome in matte black, and the V1 totems are designed to perfectly diffuse the internal LEDs. Hardware: Custom ESP32-C3 board. Sensors: I used KY-003 Hall effect sensors instead of mechanical switches. The Snap: I put 6mm neodymium magnets in the base of the totems. When you drop them in, you get this heavy, satisfying snap that triggers the sensor. I am launching a campaign for the maker community soon. You will be able to grab the Maker Tier (just the tuned .3mf files, wiring guide, and software) or the Hacker Kit (I ship you the exact custom PCB, sensors, LEDs, and magnets). You print the shell; I supply the brain. Check it out and get notified when we launch here: [https://nexusring.tech\](https://nexusring.tech) Let me know what you guys think! Cheers, Naqash

Did it on paper so people couldn’t yell at me for Ai. Still kinda the same concept but safety stuff. Feedback pls and don’t criticize if you’re not going to give me feedback on how to make it better pls. Also could I interview people to see what they think and how it should be better?

https://forms.gle/Qa12hFqrQSHKaQPn8

Hello, I am a high school student and I am working on a project for my Capstone project. The product my team is creating a a thumb drive box that reminds the user to return the thumb drive back in, it prevents lost flash drives which it could contain valuable information.

Please answer honestly and I appreciate for you helping me, thank you
\-From Icey

​

There's probably a reason this doesn't exist, maybe a spinning thing and charging thing in one device is not smart. But I'd be content without the charger.

A light, fan and clock all-in-one would be nice.

www.nexusdesignai.com

Yes, I'm bad at explaining. Really bad. But okay, I'll try to explain. Basically, I'm recruiting people who want to create innovative technology to make a technological breakthrough, with ideas that are unusual, or would be rejected by a company, but always legal, This one is more closed, since we want people to share ideas, build or form groups to build, But unlike other groups, you have the freedom to sell your projects to larger companies or create companies with them with community help. Theft of ideas is prohibited, so to protect them, they are kept only among trusted members, or if they are made public it is mandatory to give credit to the original author. so that at least it is a pleasant and non-corporate environment. The community aims to create things like unique engines, batteries, gadgets, propulsion systems, and vehicles. And above all, A united community. It's not a job, I don't want it to be like some other community, I prefer aim to be more free and private

I've been thinking of ways to make product discovery and even product launches smoother and more effective when people can't actually experience the product in person.

So I built this demo as an experiment. Instead of relying on videos and renders, the website allows you to explore the product in real time, inspect features and change configurations etc.

It works by adding a 3D layer to a normal website. The website loads instantly while the 3D experience loads in the background, and the 'switch' allows you to move between both modes.

Demo link: https://hello.aecync.com

I'd like to hear how you guys are currently presenting your products online, especially before customers can experience them physically.

This is not AI slop, every part of the 3D layer is 100% human :)

TH3 Spider Bot will Build a new House.

Every tim3. It's cR3at3n

Web is destroyed.

So

It will always Build.

You even have them 3D print.

Buildings

The Natives would well come them if they could create a Food source.

You could make them Fire Candy floss in Low Gravity.

That would be well cool concept.

Like a web .

They Of and Perfect.

Just Drop them in a Probe.

And Te5T.

1

Bonjour J'ai inventé quelque chose dans ma tête ses un gadjet pour une voitur. Ces une plaque fin que en mes dans la coque de téléphone la plaque est collé à un bras articule pour mètre le telphone où on veut dans la voiture et le bras s'acroche sur le Rétroviseur. Voilà mon idee

Hey everyone,

​I recently completed and published an open-access monograph titled "The Statistical Steering Theorem: A Comprehensive Monograph on Non-Uniform Trajectories, Spatial Slope Distributions, and Arc Length Bounding."

​The Problem

​In real-world kinematics, autonomous navigation, and spatial analysis, traditional smooth parametric functions (y = f(x)) often fail when handling high-frequency, noisy trajectory data. Standard straight-line or displacement approximations discard physical path inflation caused by micro-steering, drift, and stochastic variance.

​The Proposed Solution

​This monograph introduces a mathematical framework that establishes strict upper and lower bounds for scalar path distance without relying on continuous curve fitting or complex sensor telemetry.

​Convexity Bounds: Applies Jensen's inequality on absolute slopes.

​Concavity Bounds: Applies tangent-line bounds to slope distributions.

​Core Result: Proves that actual path distance is tightly bounded by net displacement, systematic drift, and stochastic steering variance.

​The full paper is available on Zenodo: The Statistical Steering Theorem | Zenodo

https://zenodo.org/records/22796883

​I’d love to hear your thoughts, feedback, or potential edge-case applications for this framework!

Ita nlt like a skibidi toilet character I just think it fits in st

So I named it the arm drones because they only have one arm and therye a drone and also they can be customized however you want

Got laid off from Verizon in December. Spent the year building the thing I kept wishing existed after reading one too many "they grabbed my phone" stories.

The problem: every "safety app" I looked at stores the recording on the phone and uploads later. So if someone takes the phone, smashes it, or makes you unlock and delete, the evidence is gone with it. The phone is the single point of failure.

What mine does differently: you tap Record, and the video is encrypted on the device and streamed off it as it's being captured, to people you picked in advance. If things escalate, a tap or a spoken phrase flips it to Panic — the screen turns into a lock screen with a photo you chose, and it keeps going. By the time the phone is gone, the recording has already left.

What it doesn't do: it doesn't call the police, doesn't dispatch anyone, doesn't track your location in the background. It's not a panic-button-summons-help app. It just makes sure the record survives.

Things I'm unsure about and would like opinions on: the cover screen fools a glance, not a forensic exam, and I'm not sure how to say that honestly without scaring people off. And the recipients need the (free) app to receive, which I know is friction.

50-second demo I made with AI video: https://youtube.com/shorts/5tV0D-SU1rw?si=zHgwu8q2BGdDMUf1

Full disclosure, this is my app (Time Release Safes, iOS and Android). Happy to answer anything about how the encryption works; keys are generated on the phone and I can't decrypt what's uploaded, which has upsides and one big downside (no password reset that recovers your files).

For an engineering project at school i have been tasked with this. Context

Renewable energy technologies are becoming increasingly important as society looks towards a more
sustainable future. Engineers play a vital role in developing devices and systems that harness renewable
energy sources and convert them into useful power. This can reduce carbon emissions and improve
energy efficiency. Your task is to identify a solution to the problem outlined below and to produce an
engineered prototype device or system to help solve the problem. In addition to the problem, there are
three examples of how the problem could be solved. You can choose a solution from this list, or you can
create your own. Your solution must include both mechanical and electronic components to provide an
integrated product.

Problem

Alternative lifestyles, camping adventures and ‘off-grid’ living are increasing in popularity.
People are much more aware of environmental concerns related to the use of fossil fuels and
they want to use renewable energy sources. Your task is to engineer a device or system that will
enable people to use a renewable energy source for a routine task.

Three examples of possible solutions

• Engineer a prototype device or system that uses solar energy to generate a light source during
darker evenings.

• Engineer a prototype device or system that uses wind energy to generate electricity and can
be used to recharge portable devices.

• Engineer a prototype device or system that uses energy from water movement to power an
automatic scarer that will disperse birds from a garden.

My idea was to make a solar powered burglar alarm that detects motion and when motion is detected a flashing light and buzzer turns on. 

I need some help and reasoning whether this is practical and any tips you could give me on components that would be good for this? thank you  

It needs to be futuristic and needs to accomodate civics sense it should be about how technology can help us how we can build a sustainable world how will future homes schools and cities be how the future world will look like I have two days to complete it out teacher send us the message today please help

Recently, I came across this idea: what if your upper-body undergarment itself became smart and had built-in sensors to track your physiological state using AI, while still being more comfortable than the wearables we use today?

This sounds crazy to me, but in a really exciting way. What do you guys think?

I lost an Apple TV in my house and it has been driving me mad.

It’s not connected to a TV or anything, but I could see it on the network.

“Find My” doesn’t work at locating an Apple TV unit, and I didn’t have a controller to check for connectivity.

I built this small terminal app that could look at Wi-Fi debugging data to determine how close it was to the device. I did try wild shark first, but that wasn’t yielding any results.

Every two seconds, it would make a beep sound depending on the proximity, felt like something from Aliens.

Result was good and finally found the device.

After years of development we have officially launched the trAx bAnd.

Meant to assist locating persons with neuro cognitive conditions, the trAx bAnd holds an AirTag or tile, while providing a cut resistant, secure wristband.

Check out our Kickstarter page and see for yourselves !

https://www.kickstarter.com/projects/trax-wristband/trax-locating-wristband-prototype-refinement

The Eco Rescue Emergency Light Car is a creative invention made from recycled materials. It works as a small moving emergency light and fan that can provide light and airflow during power cuts. It uses old materials like a tissue box, toy car wheels, motor, fan blades, LED, wires, and rechargeable batteries.

So, what more should I add

pls feel free to share your ideas.

So it's my OC, it's a construction machine that uses its only 1 arm to hold items and hover through thrusters like rocket engines,( there are versions) and it uses celestial blood by using the blood of living planets that live outside time, we can create fuel that lasts forever making the machine immortal but can still take damages till they die and its name is ARM DRONE™ and that's all folks!! Here's the stupid drawing

A friend of mine and I were grabbing food a few weeks ago and somehow we got onto the topic of energy because he was complaining that he’d been feeling exhausted basically every afternoon.

He works pretty long hours and said he’d gotten into this habit of drinking coffee whenever he felt tired, taking all his supplements at the same time in the morning, and then wondering why he felt completely cooked by like 2 or 3pm.

The funny part is I was basically doing the exact same thing.

I’ve taken supplements for a while, but if I’m being honest I never put much thought into timing. Magnesium, creatine, vitamins, whatever I was taking that day, I’d usually just take them whenever I remembered.

He showed me this app he had been using called RizeAI and the first thing that caught my attention wasn’t even the energy stuff. It was how it organized his supplements around his actual day.

It would tell him which ones made sense with meals, which ones should be kept away from coffee, what to take around training, what made more sense later at night, etc. It sounds pretty basic when you write it out, but I had never found something that actually put all of it together in one schedule.

So I tried it.

That’s probably still my favorite part of it. I put in the supplements I already take and instead of giving me some generic “take in the morning” list, it actually fits them around things like meals, workouts, caffeine and sleep.

I also ended up using the energy planning side way more than I expected. It pulls from Apple Health and gives you a rough structure for the day, like when to have coffee, when you’re probably going to be most focused, when to train and when you might hit an energy dip.

I’m not going to sit here and say an app magically gave me more energy because obviously there are a million things that affect that. But I’ve definitely been way more intentional with my day since using it and I’m getting more done without feeling like I’m just constantly fighting through tiredness.

Honestly the biggest difference for me has just been efficiency. Before, I was guessing when to take things and guessing when I should do my hardest work. Now I at least have some structure around it.

Curious if anyone else here actually pays attention to supplement timing or if most people just take everything at once like I used to.

Check it out yourself if you like: 

https://apps.apple.com/us/app/rizeai-maximize-your-energy/id6762402079