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<!DOCTYPE html>
<html lang="zh-Hant">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>數學探險島 - 哲學之塔</title>
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</head>
<body class="flex items-center justify-center min-h-screen p-4">
<div id="main-container" class="container mx-auto max-w-5xl">
<!-- 故事引導畫面 -->
<div id="story-view" class="bg-white/80 backdrop-blur-md rounded-xl shadow-2xl p-8 text-center">
<h1 class="text-3xl md:text-4xl font-bold text-gray-800 text-center mb-6">前情提要：西帕索斯的悲劇</h1>
<div class="border rounded-lg shadow-inner bg-gray-100 p-12 flex flex-col items-center justify-center" style="height: 50vh;">
<svg xmlns="http://www.w3.org/2000/svg" class="h-24 w-24 text-indigo-300 mb-4" fill="none" viewBox="0 0 24 24" stroke="currentColor">
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<path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M4 6h16M4 18h16" />
</svg>
<p class="text-xl text-gray-600">故事即將展開...</p>
<p class="mt-4 text-lg text-indigo-600 font-semibold">點擊下方按鈕，在新分頁閱讀故事前情提要！</p>
</div>
<p class="mt-8 text-gray-600 font-semibold">閱讀完故事後，請回來按下開始挑戰</p>
<a href="https://g.co/gemini/share/d181055c5aa2" target="_blank" id="story-link-button" class="mt-2 inline-block w-full md:w-auto bg-blue-500 text-white font-bold py-3 px-8 rounded-lg hover:bg-blue-600 transition-colors shadow-lg text-lg">
閱讀故事
</a>
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開始挑戰！
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<!-- 閱讀測驗畫面 (新增) -->
<div id="quiz-view" class="hidden bg-white/80 backdrop-blur-md rounded-xl shadow-2xl p-8">
<h1 class="text-3xl font-bold text-gray-800 text-center mb-6">閱讀測驗：西帕索斯的考驗</h1>
<div class="space-y-6 text-left">
<!-- 問題 1 -->
<div id="question-container-0" class="question-container">
<p class="font-semibold mb-2">1. 根據故事內容，西帕索斯為什麼被畢達哥拉斯囚禁在哲學之塔？</p>
<div class="space-y-2">
<label><input type="radio" name="q0" value="A" class="hidden"> <span class="quiz-option">(A) 因為他試圖偷取畢達哥拉斯的數學理論。</span></label>
<label><input type="radio" name="q0" value="B" class="hidden"> <span class="quiz-option">(B) 因為他在公開場合侮辱了畢達哥拉斯本人。</span></label>
<label><input type="radio" name="q0" value="C" class="hidden"> <span class="quiz-option">(C) 因為他發現了一個無法用分數或小數表示的數字，這與畢達哥拉斯學派的信念相衝突。</span></label>
<label><input type="radio" name="q0" value="D" class="hidden"> <span class="quiz-option">(D) 因為他沒能成功計算出一個正方形的面積。</span></label>
</div>
</div>
<!-- 問題 2 -->
<div id="question-container-1" class="question-container">
<p class="font-semibold mb-2">2. 故事中，那個動搖了畢達哥拉斯學派信念的「神秘數字」，最初是源自於什麼？</p>
<div class="space-y-2">
<label><input type="radio" name="q1" value="A" class="hidden"> <span class="quiz-option">(A) 一個面積為3的圓形半徑。</span></label>
<label><input type="radio" name="q1" value="B" class="hidden"> <span class="quiz-option">(B) 一個面積為2的正方形邊長。</span></label>
<label><input type="radio" name="q1" value="C" class="hidden"> <span class="quiz-option">(C) 一個從未有人見過的全新立體圖形。</span></label>
<label><input type="radio" name="q1" value="D" class="hidden"> <span class="quiz-option">(D) 一個畢達哥拉斯自己提出的數學謎題。</span></label>
</div>
</div>
<!-- 問題 3 -->
<div id="question-container-2" class="question-container">
<p class="font-semibold mb-2">3. 在故事的結尾，你（讀者）被賦予的主要任務是什麼？</p>
<div class="space-y-2">
<label><input type="radio" name="q2" value="A" class="hidden"> <span class="quiz-option">(A) 找到一把萬能鑰匙，趁半夜把西帕索斯從監獄裡救出來。</span></label>
<label><input type="radio" name="q2" value="B" class="hidden"> <span class="quiz-option">(B) 回到未來，尋找歷史文獻來證明西帕索斯是對的。</span></label>
<label><input type="radio" name="q2" value="C" class="hidden"> <span class="quiz-option">(C) 成為畢達哥拉斯的學徒，從內部瓦解他的學派。</span></label>
<label><input type="radio" name="q2" value="D" class="hidden"> <span class="quiz-option">(D) 找出幾個「神秘數字」的近似值，用具體的證據去說服畢達哥拉斯。</span></label>
</div>
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<button id="reread-story-button" class="w-full md:w-1/2 bg-gray-500 text-white font-bold py-3 px-6 rounded-lg hover:bg-gray-600 transition-colors">再看一次故事</button>
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<!-- 遊戲畫面 (預設隱藏) -->
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<h1 class="text-3xl md:text-4xl font-bold text-gray-800 text-center mb-2">哲學之塔</h1>
<p class="text-center text-gray-600 mb-6">幫助被囚禁的西帕索斯，找出正方形的神秘邊長！</p>
<div class="grid md:grid-cols-2 gap-8 items-center">
<!-- 左側：正方形展示區 -->
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<p class="text-2xl font-bold text-white">面積 = <span id="target-area-text">2</span></p>
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<p class="mt-4 text-2xl font-mono text-gray-700">邊長 = <span id="target-sqrt-text">√2</span></p>
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<!-- 右側：互動操作區 -->
<div class="flex flex-col space-y-6">
<div class="bg-white/80 p-4 rounded-lg text-center">
<p class="text-lg">你的猜測邊長 <span id="guess-sqrt-text" class="font-mono">√2</span> ≒ <span id="current-value" class="font-bold text-2xl text-indigo-600">1.50</span></p>
<p class="text-lg">邊長的平方(正方形面積)：<span id="current-squared-value" class="font-bold text-2xl text-red-500">2.25</span></p>
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確定答案
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挑戰下一關
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</div>
<!-- 生活應用畫面 (預設隱藏) -->
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<h1 class="text-3xl md:text-4xl font-bold text-green-600 mb-4 text-center">恭喜你，成功解救了西帕索斯！</h1>
<p class="text-lg text-gray-700 mb-8 text-center">你們玩遊戲的時候，有沒有想過，為什麼角色撞到怪物就會扣血？為什麼子彈會正好打到你？這不是靠神奇的第六感，是靠數學──而且關鍵數學招式就是平方根！</p>
<div class="bg-blue-50 p-6 rounded-lg text-left">
<h2 class="text-2xl font-bold text-indigo-600 mb-4 text-center">🎮 遊戲物理引擎裡的平方根魔法</h2>
<div class="space-y-6">
<div>
<h3 class="font-semibold text-xl mb-2">判斷「有沒有撞到」</h3>
<p>遊戲世界是由座標組成的（就像地圖上的 X、Y 點）。當角色和怪物在不同位置，遊戲必須算兩者的距離，來判斷是不是近到可以碰撞。</p>
<p class="mt-2 p-3 bg-gray-200 rounded-md text-center font-mono text-lg">距離 = √((x₁ - x₂)² + (y₁ - y₂)²)</p>
<p class="mt-2">最後那個開根號，就是讓距離變回「真實長度」。沒有平方根，遊戲根本不知道你到底是不是碰到牆、怪物、寶箱。</p>
</div>
<div>
<h3 class="font-semibold text-xl mb-2">算出移動的真速度</h3>
<p>在 3D 遊戲中，速度不只有一個方向。例如你同時向前（X 軸）+ 向右（Y 軸）移動，總速度不是單純相加，而是：</p>
<p class="mt-2 p-3 bg-gray-200 rounded-md text-center font-mono text-lg">總速度 = √(水平速度² + 垂直速度²)</p>
<p class="mt-2">這樣遊戲才能正確決定動畫快慢、物理反應強度。</p>
</div>
<div>
<h3 class="font-semibold text-xl mb-2">模擬「真實的碰撞反應」</h3>
<p>角色被怪物推一下，會往斜方向飛。遊戲會算推力向量的大小（也就是「合力長度」）來決定你飛多遠，這裡也要平方根。</p>
</div>
</div>
<div class="mt-6 pt-6 border-t">
<p class="text-xl text-center"><span class="font-bold">💡 簡單比喻：</span>「平方根在遊戲引擎裡，就像一把『距離測量尺』，沒有它，遊戲世界就不知道東西有多近、有多快，甚至不會知道你到底撞到沒。」</p>
</div>
</div>
<div class="mt-12 text-center">
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回到探險島地圖
</a>
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