Math Games - sgml/signature GitHub Wiki

A type system is a mathematical description of how to determine the category of a noun, such as:

  • proper noun
  • pronoun
  • common noun

The Egyptians, besides being peculiarly devoted to geometry, are the only people who employ it in their public records and land measures.

3-4-5 Triangle Game

Step Description
Measure and Mark Lay the rope flat on the ground. Mark the points where the knots are located to form the sides of the triangle.
Form the Triangle Arrange the rope so that one side measures 3 finger spacing, another side measures 4 finger spacing, and the "mrt" (longest side) measures 5 finger spacing.
Verify the Angle Adjust the rope to ensure the sides are taut and the knots are at the correct positions. The angle formed between the sides measuring 3 and 4 finger spacing will be a right angle. This method ensures that the cornerstone of the pyramid or any other structure has a precise right angle.

Games

Physical Math

Video Tutorials

Game Engines

Algorithms

Algorithm Description Example Wikipedia URL
Brute Force Tests every possible solution until the correct one is found. Solving puzzles by trying all possibilities. Brute-force search
Greedy Algorithm Makes the best possible choice at each step. Coin change problem Greedy algorithm
Divide and Conquer Breaks the problem into smaller subproblems, solves each independently, and combines results. Merge Sort Divide-and-conquer algorithm
Dynamic Programming Solves problems by combining solutions to subproblems and storing results to avoid redundancy. Fibonacci Sequence Dynamic programming
Backtracking Tries different solutions, abandoning paths that don’t work and backtracking to try others. Solving Sudoku Backtracking

Bible Examples

Insect Behavior Algorithm Description Wikipedia URL
Ants Foraging Ant Colony Optimization (ACO) Uses pheromone trails to find the shortest path to food sources. Ant Colony Optimization
Ants Communication Stigmergy Indirect communication through pheromones to guide others. Stigmergy
Bees Foraging Bees Algorithm Search pattern to find the best food sources. Bees Algorithm
Bees Communication Waggle Dance Communicates the location of food sources through a dance. Waggle Dance

Blogs

  1. Isometric Games - Art, Code and Maths - Wintermute Digital: This blog explores the reasons for using isometric perspectives, the complexity of building art for it, and the problem of shifting a whole codebase that references standard rectangular coordinates to isometric coordinates. Read more
  2. How to Make an Isometric Game? - 300Mind Blog: This detailed guide covers the isometric game development process, including perspective, graphics, and gameplay mechanics, offering insights into how developers can create compelling experiences for players. Read more
  3. A Step-by-Step Guide to Creating Isometric Game: This blog post explores how to create an isometric game and offers a step-by-step guide to crafting engaging gameplay and stunning visuals. Read more

Videos

  1. Why Isometric? | Art, Code and Matrix Maths | A Devlog - YouTube: This video discusses the rationale behind using isometric perspectives, the difference between real and simulated isometric projections, and the challenges of drawing in an isometric perspective. Watch on YouTube

Reverse Engineering Mathmatical Notation

  • Phonetic Notation
  • Percussion Notation
  • Latex:
\[
E = mc^2
\]

Game Aggregators

backlinks_to_arkadium:
  - name: CrazyGames
    url: https://www.crazygames.com
    description: A popular site for high-quality browser games.

  - name: AddictingGames
    url: https://www.addictinggames.com
    description: Offers thousands of free online games.

  - name: Agame
    url: https://www.agame.com
    description: Features thousands of free online games for all ages.

  - name: USA Today Games
    url: https://www.usatoday.com/games
    description: Provides a variety of free games, quizzes, and puzzles.

  - name: GamesGames
    url: https://www.gamesgames.com
    description: A site with a wide range of online games, including racing, sports, and solitaire.

Trivia

Rhetorical Math Riddles

Radical Expressions and Exponents

Celebrities

Algebra Sequences

Induction

Deduction

Geometric Shapes

Origami

Greek Symbols and Terminology

Mathematical Rules in Real Life

Absolutely! Let's reframe these mathematical concepts into word problems:

### Commutative Property Extensions

1. **Associative Property**:
   - **Addition**: Imagine you are arranging books on a shelf. Whether you put the first two books together before adding the third or add the third book to the first one first, you'll end up with the same number of books. For instance, if you have 2 fiction, 3 non-fiction, and 1 science book, combining the fiction and non-fiction books before adding the science book, or adding the science book first, will give you the same total.
   - **Multiplication**: Think about stacking boxes. If you have two groups of boxes and then stack a third group, the order in which you stack them doesn't matter. You'll end up with the same height.

2. **Distributive Property**: 
   - Imagine you are distributing candies into party bags. If you have 5 bags and each bag gets 2 chocolates and 3 candies, you can either distribute the chocolates first and then the candies or add up the chocolates and candies in each bag. The total number of sweets remains the same.

### Generalizations of PEMDAS

1. **Exponent Laws**:
   - **Product of Powers**: Think of repeatedly doubling a recipe. If you double it once and then double the result again, it's the same as if you had quadrupled the original recipe.
   - **Power of a Power**: If you have a plant that doubles its height every week and you wait three weeks, its height will be the same as if you had quadrupled it in the first week and then doubled the result.
   - **Power of a Product**: If you are painting walls and you have a certain number of walls and each wall is doubled in size, painting the larger walls is the same as painting the smaller ones twice.

2. **Logarithm Properties**:
   - **Product Rule**: If you are measuring the space needed for two types of furniture, the combined space can be found by adding the space each type takes individually.
   - **Quotient Rule**: If you divide one type of space by another, the resulting space can be found by subtracting the space taken by the second type from the space taken by the first.
   - **Power Rule**: If you have several identical sections of space, the total space they take up can be found by multiplying one section's space by the number of sections.

3. **Absolute Value Properties**:
   - If you are calculating the total distance you walked, no matter the direction, you add up the distances as positive values.
   - When adding the distances between stops on a bus route, even if some distances are negative (representing backward travel), the total distance is the sum of all positive distances.

4. **Complex Numbers**:
   - If you have a combination of real money and imaginary vouchers, adding or multiplying them follows specific rules. Adding two such combinations follows the same rules as adding real numbers, while multiplying them involves both real and imaginary parts.

### Advanced Algebraic Concepts

1. **Vector Spaces**:
   - If you have directions to multiple destinations, combining directions (vectors) follows the same rules as adding numbers.
   - Scaling a direction (multiplying a vector by a scalar) applies the same rule as multiplying a number.

2. **Matrix Operations**:
   - Adding matrices is like adding sets of numbers, following the same rules as addition.
   - Multiplying matrices involves combining rows and columns following specific rules.

3. **Groups and Rings**:
   - In a group, every action has an undo action. For example, in addition, each number has an additive inverse that brings the sum back to zero.
   - In a ring, you can add and multiply numbers following specific rules, where addition is always commutative, and multiplication is associative.

These concepts and their word problem equivalents provide a better understanding of how algebraic properties and principles apply to real-world situations. If you'd like to explore more, let me know!

Polygons and Cartesian Coordinates

Using a pizza cutter to divide a pizza into triangles or squares is a perfect example of applying Cartesian math in the kitchen. Here's how you can think about it:

### Dividing Pizza into Triangles

1. **Center as the Origin**: Imagine the center of the pizza as the origin (0,0) on a Cartesian plane. This is your starting point for slicing the pizza.

2. **Equal Angles**: To divide the pizza into equal triangular slices, you can visualize dividing the 360° circle into equal angles. For example, if you want 8 slices, each angle will be 45°.

3. **Straight Lines**: Using the pizza cutter, draw straight lines from the center (origin) to the edge of the pizza at the calculated angles. Each line represents a radius of the circle, and the segments formed will be the triangular slices.

### Dividing Pizza into Squares

1. **Grid Layout**: Visualize the pizza as a grid on a Cartesian plane. You can set up a grid where the pizza is divided into equal square sections.

2. **Horizontal and Vertical Cuts**: Determine how many squares you want. For instance, if you want a 3x3 grid, you'll need to make two horizontal and two vertical cuts. Each cut will be parallel to either the x-axis or the y-axis.

3. **Equal Spacing**: Ensure that each cut is evenly spaced. If the pizza's diameter is 12 inches, and you want 3 squares per side, each section will be 4 inches wide.

### Practical Steps

1. **Triangles**:
   - Place the pizza cutter at the center of the pizza.
   - Cut from the center to the edge at one angle.
   - Rotate the pizza cutter to the next angle (e.g., 45°) and cut again.
   - Repeat until the pizza is divided into the desired number of triangular slices.

2. **Squares**:
   - Measure and mark the spacing for your cuts along the x and y directions.
   - Make horizontal cuts first, then vertical cuts, ensuring each slice is a perfect square.

These techniques apply Cartesian coordinates and basic geometry principles to ensure your pizza is divided evenly, whether into triangles or squares. Happy slicing!