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‎index.html‎

Lines changed: 181 additions & 180 deletions
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@@ -670,193 +670,14 @@ <h3 style="margin:7px">Volume of a Cube</h3>
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</details>
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</section>
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<br><br><br><br>
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<div itemscope itemtype="https://schema.org/LearningResource https://schema.org/MathSolver">
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<meta itemprop="name" content="Core Geometric System ™">
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<meta itemprop="url" content="https://basic-geometry.github.io">
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<meta itemprop="inLanguage" content="en">
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<meta itemprop="accessibilityHazard" content="none">
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<meta itemprop="accessibilitySummary" content="Equations with figures and explanations">
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<meta itemprop="accessMode" content="textual">
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<meta itemprop="accessMode" content="visual">
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<meta itemprop="isAccessibleForFree" content="true">
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<meta itemprop="isFamilyFriendly" content="true">
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<meta itemprop="keywords" content="Core Geometric System, Exact Geometric Calculations, Analysis, Engineering Design Solutions, Computer Graphics Rendering, Algorithm Optimization, Navigation">
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<meta itemprop="educationalLevel" content="from basic to advanced">
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<meta itemprop="typicalAgeRange" content="6-18">
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="triangle">
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<h3 style="margin:7px" itemprop="eduQuestionType">Area of a Triangle</h3>
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<meta itemprop="target" content="https://basic-geometry.github.io?q={triangle_side1=3_side2=4_side3=5_area=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Triangle area formula">
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<meta itemprop="usageInfo" content="Either by base length and height, or perimeter">
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<br>
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<p itemprop="description" style="margin:12px">The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.</p>
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<p itemprop="abstract" style="margin:12px">The base of a triangle multiplied by its height equals a rectangle with twice the area of the triangle.
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<br>
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The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle.</p>
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<br>
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<div itemprop="text">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mrow>
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<mi>base</mi>
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<mo>×</mo>
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<mi>height</mi>
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</mrow>
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<mn>2</mn>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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</div>
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</div>
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<br><br>
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Triangle area formula aka Heron's formula">
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<p itemprop="description" style="margin:12px">The area of a triangle can also be calculated by the length of its sides.</p>
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<br>
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<div itemprop="usageInfo">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>S</mi>
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<mo>=</mo>
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<mi>Semi perimeter</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mrow>
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<mo>(</mo>
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<msub>
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<mi>side</mi>
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<mn>1</mn>
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</msub>
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<mo>+</mo>
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<msub>
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<mi>side</mi>
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<mn>2</mn>
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</msub>
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<mo>+</mo>
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<msub>
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<mi>side</mi>
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<mn>3</mn>
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</msub>
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<mo>)</mo>
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</mrow>
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<mn>2</mn>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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</div>
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<br><br><br>
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<div itemprop="text">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mrow>
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<msqrt>
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<mrow>
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<mi>S</mi>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>1</mn>
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</msub>
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<mo>)</mo>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>2</mn>
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</msub>
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<mo>)</mo>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>3</mn>
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</msub>
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<mo>)</mo>
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</mrow>
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</msqrt>
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</mrow>
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</mrow>
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</math>
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</div>
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</div>
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<br><br>
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<div itemprop="subjectOf" itemscope itemtype="https://schema.org/SoftwareApplication" style="margin:12px" id="triangle_area_calculator">
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<meta itemprop="name" content="Triangle Area Calculator">
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<meta itemprop="applicationCategory" content="Geometric Calculator">
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<meta itemprop="operatingSystem" content="Web">
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<meta itemprop="isAccessibleForFree" content="true">
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<meta itemprop="description" content="Calculate the area of a triangle from the lengths of its sides.">
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<meta itemprop="usageInfo" content="Enter the lengths of the sides of the triangles one by one.">
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<label for="side1">Side 1:</label>
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<input id="side1" type="number" value="1" step="any">
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<br>
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<label for="side2">Side 2:</label>
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<input id="side2" type="number" value="1" step="any">
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<br>
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<label for="side3">Side 3:</label>
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<input id="side3" type="number" value="1" step="any">
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<script>
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function triangleArea(product) {
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return Math.sqrt(product);
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}
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function updateTriangleArea() {
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const side1 = parseFloat(document.getElementById('side1').value);
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const side2 = parseFloat(document.getElementById('side2').value);
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const side3 = parseFloat(document.getElementById('side3').value);
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if (isNaN(side1) || isNaN(side2) || isNaN(side3)) {
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document.getElementById('triangle-area').innerText = '';
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return;
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}
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// Triangle validity check
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if (side1 + side2 <= side3 || side2 + side3 <= side1 || side3 + side1 <= side2) {
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document.getElementById('triangle-area').innerText = 'The sum of the length of the two shorter sides of a triangle is larger than the third one.';
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return;
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}
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const s = (side1 + side2 + side3) / 2;
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const product = s * (s - side1) * (s - side2) * (s - side3);
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const area = triangleArea(product);
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document.getElementById('triangle-area').innerText =
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`Area: ${area.toFixed(5)} square units`;
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}
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document.getElementById('side1').addEventListener('input', updateTriangleArea);
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document.getElementById('side2').addEventListener('input', updateTriangleArea);
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document.getElementById('side3').addEventListener('input', updateTriangleArea);
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</script>
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<p id="triangle-area"></p>
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</div>
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</section>
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<br><br><br><br>
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<section itemscope itemtype="http://schema.org/LearningResource" id="trigonometry" itemref="division">
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<h3 itemprop="name" style="margin:7px">Trigonometry</h3>
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<br>
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<figure class="imgbox" itemscope itemtype="http://schema.org/ImageObject">
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<img class="center-fit" src="trigonometry.png" alt="Trigonometric identities in a right triangle">
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</figure>
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<br>
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<p itemprop="about" style="margin:12px">In a right triangle the ratios between the sides and the angles are proportional.</p>
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<p itemprop="description" style="margin:12px">In a right triangle the ratios between the sides and the angles are proportional.</p>
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<br>
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<br>
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<math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML">
@@ -1645,10 +1466,190 @@ <h3 itemprop="name" style="margin:7px">Trigonometry</h3>
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return radian;
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}
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</script>
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</div>
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</section>
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<br><br><br><br>
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<div itemscope itemtype="https://schema.org/LearningResource https://schema.org/MathSolver">
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<meta itemprop="name" content="Core Geometric System ™">
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<meta itemprop="url" content="https://basic-geometry.github.io">
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<meta itemprop="inLanguage" content="en">
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<meta itemprop="accessibilityHazard" content="none">
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<meta itemprop="accessibilitySummary" content="Equations with figures and explanations">
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<meta itemprop="accessMode" content="textual">
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<meta itemprop="accessMode" content="visual">
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<meta itemprop="isAccessibleForFree" content="true">
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<meta itemprop="isFamilyFriendly" content="true">
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<meta itemprop="keywords" content="Core Geometric System, Exact Geometric Calculations, Analysis, Engineering Design Solutions, Computer Graphics Rendering, Algorithm Optimization, Navigation">
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<meta itemprop="educationalLevel" content="from basic to advanced">
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<meta itemprop="typicalAgeRange" content="6-18">
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="triangle">
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<h3 style="margin:7px" itemprop="eduQuestionType">Area of a Triangle</h3>
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<meta itemprop="target" content="https://basic-geometry.github.io?q={triangle_side1=3_side2=4_side3=5_area=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Triangle area formula">
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<meta itemprop="usageInfo" content="Either by base length and height, or perimeter">
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<br>
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<p itemprop="description" style="margin:12px">The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.</p>
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<p itemprop="abstract" style="margin:12px">The base of a triangle multiplied by its height equals a rectangle with twice the area of the triangle.
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<br>
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The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle.</p>
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<br>
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<div itemprop="text">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mrow>
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<mi>base</mi>
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<mo>×</mo>
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<mi>height</mi>
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</mrow>
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<mn>2</mn>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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</div>
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</div>
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<br><br>
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Triangle area formula aka Heron's formula">
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<p itemprop="description" style="margin:12px">The area of a triangle can also be calculated by the length of its sides.</p>
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<br>
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<div itemprop="usageInfo">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>S</mi>
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<mo>=</mo>
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<mi>Semi perimeter</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mrow>
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<mo>(</mo>
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<msub>
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<mi>side</mi>
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<mn>1</mn>
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</msub>
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<mo>+</mo>
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<msub>
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<mi>side</mi>
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<mn>2</mn>
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</msub>
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<mo>+</mo>
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<msub>
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<mi>side</mi>
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<mn>3</mn>
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</msub>
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<mo>)</mo>
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</mrow>
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<mn>2</mn>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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</div>
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<br><br><br>
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<div itemprop="text">
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<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mrow>
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<msqrt>
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<mrow>
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<mi>S</mi>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>1</mn>
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</msub>
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<mo>)</mo>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>2</mn>
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</msub>
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<mo>)</mo>
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<mo>×</mo>
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<mo>(</mo>
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<mi>S</mi>
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<mo>-</mo>
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<msub>
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<mi>side</mi>
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<mn>3</mn>
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</msub>
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<mo>)</mo>
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</mrow>
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</msqrt>
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</mrow>
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</mrow>
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</math>
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</div>
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</div>
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<br><br>
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<div itemprop="subjectOf" itemscope itemtype="https://schema.org/SoftwareApplication" style="margin:12px" id="triangle_area_calculator">
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<meta itemprop="name" content="Triangle Area Calculator">
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<meta itemprop="applicationCategory" content="Geometric Calculator">
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<meta itemprop="operatingSystem" content="Web">
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<meta itemprop="isAccessibleForFree" content="true">
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<meta itemprop="description" content="Calculate the area of a triangle from the lengths of its sides.">
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<meta itemprop="usageInfo" content="Enter the lengths of the sides of the triangles one by one.">
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<label for="side1">Side 1:</label>
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<input id="side1" type="number" value="1" step="any">
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<br>
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<label for="side2">Side 2:</label>
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<input id="side2" type="number" value="1" step="any">
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<br>
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<label for="side3">Side 3:</label>
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<input id="side3" type="number" value="1" step="any">
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<script>
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function triangleArea(product) {
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return Math.sqrt(product);
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}
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function updateTriangleArea() {
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const side1 = parseFloat(document.getElementById('side1').value);
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const side2 = parseFloat(document.getElementById('side2').value);
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const side3 = parseFloat(document.getElementById('side3').value);
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if (isNaN(side1) || isNaN(side2) || isNaN(side3)) {
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document.getElementById('triangle-area').innerText = '';
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return;
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}
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// Triangle validity check
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if (side1 + side2 <= side3 || side2 + side3 <= side1 || side3 + side1 <= side2) {
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document.getElementById('triangle-area').innerText = 'The sum of the length of the two shorter sides of a triangle is larger than the third one.';
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return;
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}
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const s = (side1 + side2 + side3) / 2;
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const product = s * (s - side1) * (s - side2) * (s - side3);
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const area = triangleArea(product);
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document.getElementById('triangle-area').innerText =
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`Area: ${area.toFixed(5)} square units`;
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}
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document.getElementById('side1').addEventListener('input', updateTriangleArea);
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document.getElementById('side2').addEventListener('input', updateTriangleArea);
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document.getElementById('side3').addEventListener('input', updateTriangleArea);
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</script>
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<p id="triangle-area"></p>
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</div>
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</section>
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="polygon">
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<h3 itemprop="eduQuestionType" style="margin:7px">Area of a regular Polygon</h3>
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<meta itemprop="target" content="https://basic-geometry.github.io?q={polygon_side_number=5_length=2_area=?}">

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