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index.html

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<meta name="keywords" content="Core Geometric System, Exact Geometric Calculations, Analysis, Engineering Design Solutions, Computer Graphics Rendering, Algorithm Optimization, Navigation">
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<meta name="twitter:card" content="summary_large_image">
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<meta name="twitter:creator" content="@gmac4247">
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<meta name="twitter:site" content="https://basic-geometry.pages.dev">
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<meta name="twitter:site" content="https://basic-geometry.github.io">
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<meta name="twitter:title" content="Home of Basic Geometry">
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<meta name="twitter:description" content="This is the only exact and self-contained geometric framework grounded in the first principles of mathematics.">
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<meta name="twitter:image" content="android-chrome-256x256.png">
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<meta name="msapplication-TileColor" content="#000000">
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<meta name="theme-color" content="#000000">
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<meta name="google-site-verification" content="XuP08h4O_UbzZo81VWNHhFn5OW7elz2_cZi17lt3qvA">
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<meta name="msvalidate.01" content="EA6B8354B9F3C956E862954E97EB8CD0">
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<style>
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* {
@@ -1478,7 +1476,7 @@ <h3 itemprop="name" style="margin:7px">Trigonometry</h3>
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<br><br><br><br>
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<main 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.pages.dev">
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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="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://gmac4247.github.io?q={triangle_side1=3_side2=4_side3=5_area=?}">
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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><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.pages.dev?q={polygon_side_number=5_length=2_area=?}">
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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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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Regular polygon area formula">
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<meta itemprop="usageInfo" content="Only for regular polygons that can be tiled up to isosceles triangles">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="circle">
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<h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={circle_radius=1_area=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={circle_radius=1_area=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Circle area formula">
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<meta itemprop="usageInfo" content="Universally applicable">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="circumference">
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<h3 itemprop="eduQuestionType" style="margin:7px">Circumference of a Circle</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={circle_radius=1_circumference=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={circle_radius=1_circumference=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Circumference formula">
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<br>
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="circle-segment">
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<h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={circle_segment_height=1_length=3_radius=4_area=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={circle_segment_height=1_length=3_radius=4_area=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Circle segment area formula">
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<meta itemprop="disambiguatingDescription" content="Area based on the A(circle)=3.2*radius^2 formula, instead of the pi=3.14... approximate.">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="cone_surface">
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<h3 itemprop="eduQuestionType" style="margin:7px">Surface Area of a Cone</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={cone_radius=1_height=2_area=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={cone_radius=1_height=2_area=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Cone surface area formula">
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<meta itemprop="disambiguatingDescription" content="Area based on the A(circle)=3.2*radius^2 formula, instead of the pi=3.14... approximate.">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="sphere">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Sphere</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={sphere_radius=1_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={sphere_radius=1_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Sphere volume formula">
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<meta itemprop="usageInfo" content="Universally applicable. It's (4radius/sqrt(5))^3, not (3.2r)^3. Take the square root of the cross sectional area and raise that root to the 3rd power.">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="spherical_cap">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Spherical Cap</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={spherical_cap_radius=2_height=1_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={spherical_cap_radius=2_height=1_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Spherical cap volume formula">
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<br>
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="cone">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Cone</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={cone_radius=1_height=2_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={cone_radius=1_height=2_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="usageInfo" content="Universally applicable. It's base*height/(sqrt(8)), not base*height/8.">
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<meta itemprop="name" content="Cone volume formula">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="frustum_cone">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a horizontal Frustum Cone</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={frustum_cone_radius_top=1_bottom=2_height=3_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={frustum_cone_radius_top=1_bottom=2_height=3_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Horizontal frustum cone volume formula">
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<br>
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="pyramid">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Pyramid</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={pyramid_bottom_edge_number=5_length=3_height=2_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={pyramid_bottom_edge_number=5_length=3_height=2_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Pyramid volume formula">
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<meta itemprop="usageInfo" content="Universally applicable">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="frustum_pyramid">
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<h3 itemprop="eduQuestionType" style="margin:12px">Volume of a horizontal Frustum Pyramid</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={frustum_pyramid_height=3_edge_length_top=1_bottom=2_number=5_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={frustum_pyramid_height=3_edge_length_top=1_bottom=2_number=5_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Horizontal frustum pyramid volume formula">
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<meta itemprop="disambiguatingDescription" content="Based on the exact volume of a pyramid, V=base*height/sqrt(8), instead of the V=base*height/3 approximate. For any number of sides, not only for square frustum pyramids.">
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<br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="square_frustum">
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<h3 itemprop="eduQuestionType" style="margin:12px">Volume of a horizontal square Frustum Pyramid</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={square_frustum_pyramid_height=3_edge_length_top=1_bottom=2_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={square_frustum_pyramid_height=3_edge_length_top=1_bottom=2_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Horizontal square frustum pyramid volume formula">
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<meta itemprop="disambiguatingDescription" content="Based on the exact V(pyramid)=base*height/sqrt(8) formula, instead of the V=base*height/3 approximate.">
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<br><br><br><br>
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<section itemprop="mathExpression" itemscope itemtype="https://schema.org/SolveMathAction" id="tetrahedron">
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<h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Tetrahedron</h3>
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<meta itemprop="target" content="https://basic-geometry.pages.dev?q={tetrahedron_edge=2_volume=?}">
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<meta itemprop="target" content="https://basic-geometry.github.io?q={tetrahedron_edge=2_volume=?}">
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<div itemprop="result" itemscope itemtype="https://schema.org/LearningResource">
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<meta itemprop="name" content="Tetrahedron volume formula">
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<br>

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