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The same seven pieces: how can they make different pictures?

同样七块板,怎么变出不同的图案?

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七(qī)块(kuài)小(xiǎo)板(bǎn)放(fàng)在(zài)桌上(zhuō shàng),能(néng)拼成(pīn chéng)一个(yī gè)正方形(zhèng fāng xíng)。

Seven small pieces on a table can fit together into a square.

换(huàn)一(yī)种(zhǒng)摆法(bǎi fǎ),它们(tā men)又(yòu)能(néng)拼出(pīn chū)像(xiàng)动物(dòng wù)一样(yī yàng)的(de)图案(tú àn)。

Arrange them differently, and they can form a shape that looks like an animal.

小(xiǎo)板(bǎn)没有(méi yǒu)变(biàn),图案(tú àn)怎么(zěn me)就(jiù)变(biàn)了(le)?

The pieces have not changed, so how has the picture changed?

这(zhè)就(jiù)是(shì)七巧板(qī qiǎo bǎn):一(yī)套(tào)只(zhǐ)有(yǒu)七(qī)块(kuài)板(bǎn)的(de)拼图(pīn tú)玩具(wán jù)。

This is tangram: a puzzle toy with just seven pieces.

其中(qí zhōng)有(yǒu)两个(liǎng gè)大(dà)三角形(sān jiǎo xíng)、一个(yī gè)中(zhōng)三角形(sān jiǎo xíng)和(hé)两个(liǎng gè)小(xiǎo)三角形(sān jiǎo xíng)。

They include two large triangles, one medium triangle, and two small triangles.

另外(lìng wài)两(liǎng)块(kuài),是(shì)一(yī)个(gè)正方形(zhèng fāng xíng)和(hé)一(yī)个(gè)平行四边形(píng xíng sì biān xíng)。

The other two pieces are a square and a parallelogram.

平行四边形(píng xíng sì biān xíng)有(yǒu)两(liǎng)组(zǔ)对边(duì biān);同一(tóng yī)组(zǔ)的(de)两(liǎng)条(tiáo)边(biān)沿(yán)直线(zhí xiàn)延长(yán cháng),也(yě)不(bù)会(huì)相交(xiāng jiāo)。

A parallelogram has two pairs of opposite sides; the two sides in each pair will not meet even when extended in straight lines.

玩(wán)的(de)时候(shí hòu),要(yào)用上(yòng shàng)全部(quán bù)七(qī)块(kuài),不(bù)把(bǎ)它们(tā men)叠(dié)起来(qǐ lái),拼出(pīn chū)与(yǔ)样图(yàng tú)相同(xiāng tóng)的(de)外形(wài xíng)。

To play, you use all seven pieces without overlap to make the same outline as the example picture.

你(nǐ)可以(kě yǐ)移动(yí dòng)小(xiǎo)板(bǎn),也(yě)可以(kě yǐ)转动(zhuàn dòng)它们(tā men),改变(gǎi biàn)每(měi)块(kuài)板(bǎn)的(de)方向(fāng xiàng)。

You can move the pieces or rotate them to change the direction each one faces.

位置(wèi zhì)和(hé)方向(fāng xiàng)一(yī)变(biàn),拼出来(pīn chū lái)的(de)外边缘(wài biān yuán)也(yě)可能(kě néng)跟着(gēn zhe)变(biàn)。

When their positions and directions change, the outer outline of the arrangement may change too.

一(yī)个(gè)角(jiǎo)可能(kě néng)让(ràng)人(rén)想到(xiǎng dào)头(tóu),另一(lìng yī)处(chù)可能(kě néng)让(ràng)人(rén)想到(xiǎng dào)尾巴(wěi bā)。

One corner might suggest a head, while another part might suggest a tail.

这些(zhè xiē)小(xiǎo)板(bǎn)就(jiù)不再(bù zài)只是(zhǐ shì)几(jǐ)块(kuài)三角形(sān jiǎo xíng)和(hé)四边形(sì biān xíng),而(ér)成(chéng)了(le)一(yī)个(gè)可以(kě yǐ)认出来(rèn chū lái)的(de)图案(tú àn)。

The pieces become more than a few triangles and quadrilaterals: they form a recognizable picture.

还(hái)有(yǒu)一(yī)个(gè)有意思(yǒu yì sī)的(de)地方(dì fāng):图案(tú àn)变(biàn)了(le),小(xiǎo)板(bǎn)本身(běn shēn)的(de)大小(dà xiǎo)却(què)没(méi)变(biàn)。

There is another interesting detail: the picture changes, but the pieces themselves stay the same size.

只要(zhǐ yào)用(yòng)的(de)还是(hái shì)这(zhè)七(qī)块(kuài)、不(bù)叠(dié)在(zài)一起(yī qǐ),它们(tā men)在(zài)桌上(zhuō shàng)盖住(gài zhù)的(de)总面积(zǒng miàn jī)就(jiù)一样(yī yàng)。

As long as you use the same seven pieces without overlap, the total area they cover on the table stays the same.

这里(zhè lǐ)说(shuō)的(de)是(shì)小板(xiǎo bǎn)实际(shí jì)盖住(gài zhù)的(de)地方(dì fāng),不(bù)包括(bāo kuò)图案(tú àn)中间(zhōng jiān)的(de)空隙(kòng xì)。

This means the space actually covered by the pieces, excluding any gaps within the arrangement.

原来(yuán lái),七巧板(qī qiǎo bǎn)变出(biàn chū)的(de)新(xīn)图案(tú àn),来自(lái zì)新(xīn)的(de)组合(zǔ hé),而(ér)不是(bù shì)更多(gèng duō)的(de)小(xiǎo)板(bǎn)。

So tangram's new pictures come from new combinations, rather than additional pieces.

Written by QI Chinese for Chinese learners.

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