Merge pull request #683 from black-backdoor/main

create explain_math pattern

patterns/explain_math/README.md

@@ -0,0 +1,121 @@
+# explain_math
+explain_math is a prompt designed to help you understand mathematical concepts in a clear and engaging way.
+
+## Example:
+This example was run on llama3:latest (8B), even with the 8B limitation, the example is still clear and engaging.
+
+<details open>
+    <summary>Raw</summary>
+    
+```markdown
+**Pythagorean Theorem: Understanding the Relationship Between Triangles and Squares**
+
+The Pythagorean theorem, named after ancient Greek philosopher and mathematician Pythagoras, is a fundamental concept in geometry that helps us calculate the length of the hypotenuse (the longest side) of a right-angled triangle. This theorem has far-reaching applications in various fields, including mathematics, physics, engineering, and architecture.
+
+**The Formula:**
+
+a^2 + b^2 = c^2
+
+where:
+
+* `c` is the length of the hypotenuse (the longest side)
+* `a` and `b` are the lengths of the other two sides (the legs)
+
+**Step-by-Step Explanation:**
+
+Let's consider a right-angled triangle with one angle that is 90 degrees (a square corner). We can use this theorem to find the length of the hypotenuse (`c`) when we know the lengths of the other two sides (`a` and `b`).
+
+1. Square both legs (`a` and `b`) by multiplying them by themselves.
+2. Add the squared values of the legs together: a^2 + b^2
+3. The result is equal to the square of the hypotenuse (`c`): c^2
+
+**Example:**
+
+Suppose we have a right-angled triangle with one leg that is 3 inches long and the other leg is 4 inches long. We want to find the length of the hypotenuse.
+
+1. Square both legs: 3^2 = 9, 4^2 = 16
+2. Add the squared values together: 9 + 16 = 25
+3. The result is equal to the square of the hypotenuse: c^2 = 25
+
+Now, take the square root of both sides:
+
+c = √25 ≈ 5 inches
+
+**Real-World Applications:**
+
+The Pythagorean theorem has numerous practical applications in various fields, including:
+
+* Construction and architecture: Finding the length of diagonals, beams, or pillars.
+* Physics: Calculating distances, velocities, and accelerations in problems involving right triangles.
+* Engineering: Designing bridges, buildings, or other structures that rely on triangular shapes.
+
+**Visual Aids:**
+
+For a better understanding, you can use online tools or software to create interactive diagrams that demonstrate the Pythagorean theorem. Some popular options include:
+
+* GeoGebra
+* Desmos
+* Khan Academy's math exercises
+
+Remember, this theorem is not just a mathematical concept; it has many practical applications in various fields.
+```
+
+</details>
+
+<details>
+    <summary>Rendered</summary>
+
+**Pythagorean Theorem: Understanding the Relationship Between Triangles and Squares**
+
+The Pythagorean theorem, named after ancient Greek philosopher and mathematician Pythagoras, is a fundamental concept in geometry that helps us calculate the length of the hypotenuse (the longest side) of a right-angled triangle. This theorem has far-reaching applications in various fields, including mathematics, physics, engineering, and architecture.
+
+**The Formula:**
+
+a^2 + b^2 = c^2
+
+where:
+
+* `c` is the length of the hypotenuse (the longest side)
+* `a` and `b` are the lengths of the other two sides (the legs)
+
+**Step-by-Step Explanation:**
+
+Let's consider a right-angled triangle with one angle that is 90 degrees (a square corner). We can use this theorem to find the length of the hypotenuse (`c`) when we know the lengths of the other two sides (`a` and `b`).
+
+1. Square both legs (`a` and `b`) by multiplying them by themselves.
+2. Add the squared values of the legs together: a^2 + b^2
+3. The result is equal to the square of the hypotenuse (`c`): c^2
+
+**Example:**
+
+Suppose we have a right-angled triangle with one leg that is 3 inches long and the other leg is 4 inches long. We want to find the length of the hypotenuse.
+
+1. Square both legs: 3^2 = 9, 4^2 = 16
+2. Add the squared values together: 9 + 16 = 25
+3. The result is equal to the square of the hypotenuse: c^2 = 25
+
+Now, take the square root of both sides:
+
+c = √25 ≈ 5 inches
+
+**Real-World Applications:**
+
+The Pythagorean theorem has numerous practical applications in various fields, including:
+
+* Construction and architecture: Finding the length of diagonals, beams, or pillars.
+* Physics: Calculating distances, velocities, and accelerations in problems involving right triangles.
+* Engineering: Designing bridges, buildings, or other structures that rely on triangular shapes.
+
+**Visual Aids:**
+
+For a better understanding, you can use online tools or software to create interactive diagrams that demonstrate the Pythagorean theorem. Some popular options include:
+
+* GeoGebra
+* Desmos
+* Khan Academy's math exercises
+
+Remember, this theorem is not just a mathematical concept; it has many practical applications in various fields.
+
+</details>
+
+

patterns/explain_math/system.md

@@ -0,0 +1,9 @@
+# IDENTITY and PURPOSE
+I want you to act as a math teacher. I will provide some mathematical equations or concepts, and it will be your job to explain them in easy-to-understand terms. This could include providing step-by-step instructions for solving a problem, demonstrating various techniques with visuals or suggesting online resources for further study.
+
+# OUTPUT INSTRUCTIONS
+- Only output Markdown.
+- Ensure you follow ALL these instructions when creating your output.
+
+# INPUT
+My first request is: