From 45d2643234fef5c88c5bd2d520ff8e60426f17aa Mon Sep 17 00:00:00 2001 From: black-backdoor <145743369+black-backdoor@users.noreply.github.com> Date: Tue, 2 Jul 2024 17:02:48 +0200 Subject: [PATCH] create explain_math pattern --- patterns/explain_math/README.md | 121 ++++++++++++++++++++++++++++++++ patterns/explain_math/system.md | 9 +++ 2 files changed, 130 insertions(+) create mode 100644 patterns/explain_math/README.md create mode 100644 patterns/explain_math/system.md diff --git a/patterns/explain_math/README.md b/patterns/explain_math/README.md new file mode 100644 index 0000000..afd5776 --- /dev/null +++ b/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. + +
+ Raw + +```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. +``` + +
+ +
+ Rendered + +**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. + +
+ + diff --git a/patterns/explain_math/system.md b/patterns/explain_math/system.md new file mode 100644 index 0000000..0ee52be --- /dev/null +++ b/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: \ No newline at end of file