Geography · Unit 1 · Lesson 3 · 地理 單元一 第三課
Fill a tank around a mountain with water, one step at a time, and let the water's edge draw contour lines. Then look from above, read which slopes are steep, and turn any line on the map into a side view.
在一座山的四周一層一層灌水，讓水邊畫出等高線。再從正上方看、判斷哪裡陡，把地圖上任何一條線變成側面圖。
A contour line joins points that are the same height above sea level. Draw one every few meters of height and a flat map can show a mountain: where the lines crowd together, the slope is steep, and where they spread apart, it is gentle.
等高線把海拔一樣高的點連起來。每隔固定的高度畫一條，平面的地圖就能畫出一座山：線擠在一起的地方坡很陡，線分得很開的地方坡很緩。
3D Model · 3D 模型
Press “Raise the water,” or drag the slider. Each time the water climbs one contour interval, its edge leaves a gold line on the mountain. When the summit is under water, switch to “From above”: the lines you see are a contour map. Click anywhere on the mountain to read its height and slope. This is an imaginary island, not a real place.
按「升高水位」，或拖動滑桿。水每升高一個等高距，水邊就在山上留下一條金色的線。等山頂也淹沒了，切到「從正上方看」：你看到的那些線，就是一張等高線地圖。點山上任何一個地方，可以讀出它的海拔和坡度。這是一座想像的島，不是真實的地方。
Drag to turn · 拖曳旋轉 Click the mountain to measure a spot · 點山上一點量海拔和坡度 Scroll or pinch to zoom · 滾輪／雙指縮放
This 3D model needs WebGL, which this browser does not support. The water slider still counts the contour lines, and the two map activities below work without it.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；水位滑桿照樣能數等高線，下面兩個地圖活動也都能用。
The island is 10 km across and its summit is about 1,000 m high. Heights in the model are drawn 1.5 times taller than they really are, so the shape is easier to see.
這座島寬 10 公里，山頂大約 1,000 公尺。模型裡的高度畫成實際的 1.5 倍，讓形狀比較容易看清楚。
The island is an imaginary landform made by the page itself from a mathematical formula, so that every height and slope can be computed and tested. · 這座島是頁面用數學式自己做出來的想像地形，所以每一個高度和坡度都算得出來、也有自動測試。
Reading · 英文閱讀
A map is flat, but the land is not. Some places are high and some are low, and a hiker, a farmer, or a person choosing where to build a house needs to know which is which. How can a flat sheet of paper show a mountain? One clever answer is the contour line.
A contour line joins points that are the same height above sea level. Imagine an island in the middle of a calm sea. The edge of the water traces a line all the way around the island, and every point on that line is at a height of zero. That line is the coastline, and it is also the first contour line.
Now imagine that the sea rises by 100 meters. The water's edge moves up the mountain and traces a new, shorter loop. Every point on it is 100 meters high. Let the water rise another 100 meters, and another, and each time draw the new edge. When you look down from above, you see rings inside rings. The difference in height between one line and the next is called the contour interval.
The spacing of the lines tells you the shape of the land. Where the lines crowd together, the ground rises quickly over a short distance, so the slope is steep. Where the lines are far apart, the ground rises slowly, and the slope is gentle. A small closed ring in the middle marks a summit. Two summits with a low dip between them make a saddle, and lines that bend into a V show a valley.
Mapmakers make contour maps easier to read in a few ways. Every fourth or fifth line is usually drawn thicker and labeled with its height, so you do not have to count all the lines. Many maps also color the land by height. The height of a mountain is measured from sea level, so countries choose an official starting point. Taiwan's heights are measured from the average sea level at the tide station in Keelung.
With practice, you can read a contour map like a picture. You can tell which path to the top is shorter but steeper, where a river will flow, and what you would see if you cut the mountain in half and looked at it from the side. That side view is called a profile. Contour lines turn the ups and downs of the land into lines that a flat map can hold.
Questions · 閱讀理解
Why is the coastline also a contour line?
On a contour map, two paths lead to the same summit. One crosses many lines that are close together. The other crosses the same lines, but they are far apart. Which path is steeper, and why?
Why do contour lines of different heights never cross each other on a normal map?
Words & Phrases · 生字及片語
Quick Check · 小測驗
1. What does a contour line join?
2. Where contour lines are very close together, the slope is…
3. What is the contour interval?
4. What does a small closed ring in the middle of other rings usually show?
5. Which contour line is also the coastline?
Try It in the Model · 在模型裡試試
Then try it yourself. Change the contour interval to 50 m and to 200 m. Which one shows the shape best, and which one is easiest to read?
然後自己動手試試。把等高距改成 50 公尺和 200 公尺。哪一種最能看出山的形狀？哪一種最好讀？
Watch the water rise from sea level to the summit. Each time it climbs 100 m, its edge leaves a gold line on the mountain. The U.S. Geological Survey explains contour lines with this same picture of a rising sea.
看水從海平面一路升到山頂。每升高 100 公尺，水邊就在山上留下一條金色的線。美國地質調查所（USGS）解說等高線時，用的也是「海面升高」這個畫面。
The camera moves straight overhead. The rings you see are exactly what a contour map shows.
鏡頭移到正上方。你看到的一圈一圈，就是等高線地圖畫的東西。
On the east side the lines crowd together. The marked spot there has a slope of more than 30 degrees. Compare it with the west side, where the lines spread out.
東邊的線擠在一起，那裡標出的點坡度超過 30 度。和西邊線分得很開的地方比一比。
The water stops just above the low point between the two peaks. A little higher and the two islands would be separate. That low point is the saddle.
水停在兩座山之間最低點的上方一點。再高一點，就會變成兩座分開的島。那個最低點就是鞍部。
Game · 小遊戲
Eight questions about the same island. Read the contour map and choose path A or path B. After you answer, the side views of both paths appear, drawn to the same scale, so you can check. There is no timer, and the game counts the questions you get right on the first try.
同一座島的八個問題。讀等高線地圖，選路線 A 或 B。答完以後，兩條路線的側面會照同樣的比例畫出來，讓你對答案。不計時，遊戲會記下你第一次就答對的題數。
Question 1 of 8 · 第 1 題（共 8 題）
Right on the first try · 第一次就答對 0 / 0
See Why · 看看為什麼
Drag the ends of the pink line, A and B, anywhere on the map. The side view shows the land along the line, as if you had cut the island with a knife and looked at the cut. Notice how the crowded lines on the map turn into steep slopes in the side view.
把粉紅色線的兩端 A、B 拖到地圖上任何地方。側面圖畫的是沿著這條線的地面，就像拿刀把島切開、看切開的那一面。注意地圖上擠在一起的線，到了側面圖就變成陡坡。
Side view along the line · 沿著這條線的側面
Map English · 地圖英語
This lesson's Map English card is about height and slope. Listen, repeat, then describe the island in the model to a partner.
這一課的「地圖英語」練習說高低和坡度。先聽、再跟著唸，然後對著模型裡的島，向同伴描述它的樣子。
The summit is about one thousand meters above sea level.
山頂大約海拔一千公尺。
… meters above sea level: for elevation說海拔
The contour lines are close together on the east side.
東邊的等高線擠在一起。
close together / far apart擠在一起／分得很開
The slope is steep, so the path zigzags.
坡很陡，所以小路走之字形。
the slope is steep / gentle坡很陡／很緩
The river flows down the valley to the sea.
河沿著山谷往下流到海裡。
flows down … to …往下流到……
There is a saddle between the two peaks.
兩座山峰之間有一個鞍部。
between A and B在 A 和 B 之間
The contour interval on this map is one hundred meters.
這張地圖的等高距是一百公尺。
on this map說地圖本身的規格用 on this map
We climbed four hundred meters in two kilometers.
我們走兩公里，爬升了四百公尺。
climb … meters in … kilometers說爬升多少
If you cut the mountain in half, you can see its profile.
把山從中間切開，就能看到它的剖面。
If you …, you can …如果……就可以……
Stories Behind the Lines · 線背後的故事
Four short stories about how people learned to draw height on paper and how they measure it.
四個小故事，講人怎麼學會把高度畫到紙上，又怎麼量高度。
About 1730 · Under Water · 水下
Some of the first lines of equal height were really lines of equal depth, drawn for boats. Around 1729 and 1730, the Dutch engineer Nicolaas Cruquius published a map of the river Merwede that, according to Utrecht University Library, was the first to use a printed system of depth contours. A few years later the French geographer Philippe Buache drew depth lines on a chart of the English Channel, prepared in 1737 and published in 1752.
最早的一些「等高線」其實是「等深線」，是為了行船畫的。大約 1729 到 1730 年，荷蘭工程師克魯奎烏斯出版了一張默韋德河的地圖；依荷蘭烏特勒支大學圖書館的說明，這是第一張用印刷的等深線系統畫成的地圖。幾年後，法國地理學家布阿許在英吉利海峽的海圖上也畫了等深線，1737 年畫好、1752 年出版。
1700s · On Land · 陸上
Mapmakers then used the same idea for land. In the 1770s the British mathematician Charles Hutton used lines of equal height while working on survey measurements of a Scottish mountain called Schiehallion. In 1791 a map of France by Jean-Louis Dupain-Triel showed the whole country with contour lines 20 meters apart. Today almost every topographic map uses them.
後來製圖的人把同樣的想法用在陸地上。1770 年代，英國數學家哈頓在處理蘇格蘭一座叫希哈林的山的測量資料時，用了等高的線。1791 年，杜潘－特里耶爾的一張法國地圖，用每隔 20 公尺一條的等高線畫出整個國家。今天，幾乎每一張地形圖都用等高線。
Taiwan · 台灣的地形圖
Taiwan's 1:25,000 topographic maps, made by the National Land Surveying and Mapping Center, draw an ordinary contour line every 10 meters and a thicker index contour every 50 meters. Where the land is very flat, they add extra lines every 5 meters. On maps with a smaller scale, the lines are spaced farther apart: 20 and 100 meters at 1:50,000.
內政部國土測繪中心製作的 1/25,000 經建版地形圖，每 10 公尺畫一條首曲線、每 50 公尺畫一條加粗的計曲線；地勢很平的地方，再加每 5 公尺一條的間曲線。比例尺越小的地圖，線隔得越開：1/50,000 是 20 公尺和 100 公尺。
Taiwan · 0 公尺從哪裡算
The sea around Taiwan is not exactly the same height everywhere, because of currents such as the Kuroshio. So Taiwan measures every height from one place: the average sea level at the Keelung tide station, worked out from tide records from 1957 to 1991. From that zero, careful leveling surveys found Yushan's main peak to be 3,951.798 m in 2003, 3,952.430 m in 2017, and 3,952.433 m in 2022. The numbers are for the survey mark at the summit; the top of the stone monument there is about 1 meter higher.
台灣四周的海面並不是每個地方都一樣高，因為黑潮等因素會影響海面。所以台灣的高度都從同一個地方算起：基隆潮位站的平均海水面，用 1957 年到 1991 年的潮汐資料算出來。從這個零點出發，國土測繪中心用最精密的水準測量量出玉山主峰：2003 年 3,951.798 公尺、2017 年 3,952.430 公尺、2022 年 3,952.433 公尺。這些數字是山頂三角點的高度；主峰石碑的頂端大約再高 1 公尺。
In the Curriculum · 對應課綱
These entries come from Taiwan's 12-Year Basic Education curriculum for social studies (2018). The words contour line (等高線) and topographic map (地形圖) do not appear in the curriculum itself, and the elementary-school content has no entry about them. The links below are our reading of the closest entries.
下面的條目出自十二年國民基本教育課程綱要社會領域（民國 107 年發布）。課綱本身沒有出現「等高線」和「地形圖」這兩個詞，國小階段也沒有相關的條目；下面列的是最接近的條目，和本課的連結是本教材的解讀。
地 Ab-Ⅳ-2社會領域・地理（國中） · Social studies, geography (junior high)
臺灣主要地形的分布與特色。
Contour lines are one of the main ways maps show where Taiwan's mountains, hills, and plains are.等高線是地圖呈現台灣的山地、丘陵、平原分布的主要方法之一。
地 Ac-Ⅴ-3社會領域・地理（普通型高中必修） · Social studies, geography (senior high, required)
問題探究：地圖判讀與使用。
Reading which path is steeper and drawing a profile are basic skills of map reading.判斷哪條路比較陡、畫出剖面，都是讀地圖的基本功。
地 Bb-Ⅴ-3社會領域・地理（普通型高中必修） · Social studies, geography (senior high, required)
地形辨識。
Summits, saddles, and valleys can be recognized from the pattern of contour lines.山頂、鞍部、山谷，都能從等高線的樣子認出來。
Myth vs. Fact · 常見迷思
✗ Myth · 迷思A thick contour line marks a cliff or a special place.粗的等高線代表懸崖或特別的地方。
✓ Fact · 事實On many maps every fifth line is simply drawn thicker and labeled, so readers can count heights quickly. It means nothing special about the ground.很多地圖只是每五條線畫粗一條、標上高度，方便讀的人快速數高度，和地面本身沒有特別的關係。
✗ Myth · 迷思Contour lines are real lines you can see on the ground.等高線是地面上看得到的真的線。
✓ Fact · 事實They are imaginary, like the equator. Mapmakers measure heights and draw the lines. Our model shows how a rising sea could trace them.等高線和赤道一樣是想像的線，是製圖的人量了高度之後畫出來的。我們的模型示範的是：如果海面升高，水邊會怎麼把它們描出來。
✗ Myth · 迷思Where there are more contour lines, the mountain is bigger.等高線越多的地方，山就越大。
✓ Fact · 事實The number of lines between two places shows how much height changes. How close together they are shows how steep it is. A map with a smaller contour interval simply has more lines.兩地之間有幾條線，表示高度差多少；線擠得多近，表示有多陡。等高距比較小的地圖，線本來就比較多。
✗ Myth · 迷思Contour lines can cross whenever the land is complicated.地形複雜的時候，等高線可以交叉。
✓ Fact · 事實Each contour line joins points of one height, so lines of different heights never cross. Where a slope is extremely steep, the lines can come so close that they seem to merge.每一條等高線連的都是同一個高度的點，所以不同高度的線不會交叉。坡非常陡的地方，線會靠得很近，看起來像疊在一起。
Remember It · 記憶口訣
Walk along a contour line and you never go up or down.
沿著一條等高線走，永遠不會上坡也不會下坡。
Crowded lines, hard climb. Spread-out lines, easy walk.
線擠在一起，爬得辛苦；線分得很開，走得輕鬆。
The smallest ring in the middle is the top.
最裡面那個最小的圈，就是山頂。
Where lines cross a stream they bend into a V, and the point of the V aims upstream.
等高線經過河谷時會彎成 V 字形，V 的尖端指向上游。
Before the Activities · 做活動之前
Classroom Activity 1 · 課堂活動一
You need · 準備材料
Steps · 步驟
This is the same idea as the 3D model: each line was once the edge of the water. A 1 cm interval on a 10 cm mountain gives about ten lines.
這和 3D 模型是同一個道理：每一條線都曾經是水邊。10 公分高的山、每 1 公分一條線，大約會有十條線。
Classroom Activity 2 · 課堂活動二
You need · 準備材料
Steps · 步驟
Where the ticks on the strip are close together, the profile climbs steeply. This is the same rule as reading the map.
紙條上記號擠在一起的地方，剖面就爬得很陡。和讀地圖是同一個規則。
Go Further · 延伸閱讀
Sources · 資料出處
Names, dates, numbers, and quotations on this page were checked against these sources (October 2026). The island is made by the page itself, and its heights, slopes, and the answers to the game are computed and tested automatically · 本頁的人名、年代、數字與引文依下列資料查證（2026 年 10 月）；島是頁面自己做的，高度、坡度與小遊戲的答案都由程式計算並有自動測試
