mirror of
https://github.com/HananoshikaYomaru/openfreebooks.git
synced 2026-11-13 04:55:51 +00:00
60 lines
2.6 KiB
HTML
60 lines
2.6 KiB
HTML
<div class="book-prose">
|
|
<h2 id="history" class="book-prose__heading">History</h2>
|
|
<p>
|
|
The theorem is named after Pythagoras, but knowledge of right-triangle relationships existed in
|
|
earlier Babylonian and Indian mathematics. It became central in Euclidean geometry and later in
|
|
coordinate methods.
|
|
</p>
|
|
|
|
<h2 id="derivation" class="book-prose__heading">Derivation and reasoning</h2>
|
|
<h3 id="area-idea" class="book-prose__heading">Area-based proof idea</h3>
|
|
<p>
|
|
A classic proof rearranges four identical right triangles inside a square in two different ways.
|
|
Equating uncovered areas leads to \(a^2+b^2=c^2\).
|
|
</p>
|
|
|
|
<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Find hypotenuse if legs are 9 and 12.</summary>
|
|
<div class="book-question__solution">
|
|
<p><strong>Answer:</strong> \(c=\sqrt{9^2+12^2}=\sqrt{225}=15\).</p>
|
|
</div>
|
|
</details>
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">A right triangle has hypotenuse 17 and one leg 8. Find the other leg.</summary>
|
|
<div class="book-question__solution">
|
|
<p><strong>Answer:</strong> \(\sqrt{17^2-8^2}=\sqrt{225}=15\).</p>
|
|
</div>
|
|
</details>
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Are sides 10, 24, 26 right-angled?</summary>
|
|
<div class="book-question__solution">
|
|
<p><strong>Answer:</strong> Yes, \(10^2+24^2=100+576=676=26^2\).</p>
|
|
</div>
|
|
</details>
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Distance between \((-2,1)\) and \((4,9)\).</summary>
|
|
<div class="book-question__solution">
|
|
<p><strong>Answer:</strong> \(\sqrt{6^2+8^2}=10\).</p>
|
|
</div>
|
|
</details>
|
|
<details class="book-question">
|
|
<summary class="book-question__prompt">Rectangle has side lengths 7 and 24. Find diagonal.</summary>
|
|
<div class="book-question__solution">
|
|
<p><strong>Answer:</strong> \(\sqrt{7^2+24^2}=25\).</p>
|
|
</div>
|
|
</details>
|
|
|
|
<h2 id="applications" class="book-prose__heading">Applications</h2>
|
|
<ul>
|
|
<li><strong>Architecture:</strong> checking right angles and structural diagonals.</li>
|
|
<li><strong>Navigation:</strong> shortest displacement calculations on grid maps.</li>
|
|
<li><strong>Computer graphics:</strong> pixel distance and vector magnitude.</li>
|
|
</ul>
|
|
|
|
<h2 id="references" class="book-prose__heading">References</h2>
|
|
<ul>
|
|
<li>Standard high-school geometry curricula on Pythagoras and its converse.</li>
|
|
<li>Classical Euclidean geometry references.</li>
|
|
</ul>
|
|
</div>
|