ฝึกพูดภาษาอังกฤษด้วยเทคนิค Shadowing จากวิดีโอ: This structure feels impossible to move

This is a strange one.

It's Jessen's octahedron, infinitesimally flexible.

What does that mean?

Well, if you think about a structure like this one, if this was perfectly rigid, then there would be no movement at all.

But in the real world, these bars would be a little bit stretchy, which means that I can pull up on this joint.

And if I were to plot the lengthening of this rod against the vertical motion of the joint, it would look like this.

You can't move the joint without stretching the bar.

But what about a structure like this?

The curve flattens out zero movement.

So at the very beginning, it's possible to move that joint without the bar lengthening at all.

But then as soon as the joint does move, the bar will have to lengthen.

A structure like this is infinitesimally flexible, but because it exists in the real world, I can actually flex it.

And it feels like it takes no force to do so until it has traveled some distance.

Whereas with this structure, it feels like I can't move it at all.

It's easy to make an infinitesimally flexible joint.

You just take a straight rod and you put the joint in the middle Similarly,

in three dimensions, a polyhedron will be infinitesimally flexible if one of the vertices is coplanar,

whereas Jessen's polyhedron is able to achieve infinitesimal flexibility without having to resort to coplanar vertices.

When I squeeze it, I can feel air coming out.

And incredibly, that's actually proof that Jessen's polyhedron isn't a true flexible polyhedron.

Robert Connolly discovered the first proper flexible polyhedron in 1977.

It's this monster with 18 faces.

Annelly proved that the volume of a flexible polyhedron doesn't change as the polyhedron flexes.

It's called the bellows conjecture because a polyhedron cannot be used as bellows.

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Vocabulary and speaking notes for this lesson

This C1 speaking lesson is built on the video “This structure feels impossible to move”. The speaker keeps coming back to these words: polyhedron, flexible, joint, infinitesimally, structure. This video has 24 sentences and 307 words to shadow. The speech runs for 1:41. The speaker talks fast, about 182 words per minute, so expect linked and reduced sounds. Only 75% of the words are among the 3,000 most common in English, so the vocabulary is demanding.

Key vocabulary in this video

The 15 most advanced words in the video, with pronunciation and meaning:

Word	Pronunciation	Meaning
polyhedron noun	/ˌpɒlɪˈhiːdɹən/	A solid figure with many flat faces and straight edges.
infinitesimally adverb		In an infinitesimal manner.
lengthen verb	/ˈlɛŋθən/	To make longer, to extend the length of.
bellows noun	/ˈbɛl.oʊz/	A device for delivering pressurized air in a controlled quantity to a controlled location. At its most simple terms a bellows is a container which is…
coplanar adjective	/kəʊˈpleɪnə(ɹ)/	Within the same plane.
vertex noun	/ˈvɝˌtɛks/	The highest point, top or apex of something.
flex verb	/flɛks/	To bend something.
conjecture noun	/kənˈd͡ʒɛkt͡ʃə/	A statement or an idea which is unproven, but is thought to be true; a guess.
flatten verb	/ˈflæ.tən/	To make something flat or flatter.
infinitesimal adjective	/ˌɪnfɪnɪˈtɛsɪməl/	Incalculably, exceedingly, or immeasurably minute; vanishingly small.
octahedron noun		a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.
stretchy adjective	/ˈstɹɛt͡ʃi/	Capable of stretching; elastic.
rigid adjective	/ˈɹɪd͡ʒ.ɪd/	Stiff, rather than flexible.
squeeze verb	/skwiːz/	To apply pressure (to something) from two or more sides at once.
flexibility noun	/ˌflɛksɪˈbɪlɪti/	The quality of being flexible, whether physically or metaphorically.

Phrasal verbs you will hear

Word	Pronunciation	Meaning
come out verb	/ˌkʌm ˈaʊt/	To be discovered; to be revealed.

Pronunciation to watch

The speaker uses 4 contractions and reduced forms, such as can't, doesn't, isn't. Say them the short way, as you hear them.

Long words — get the stress right: polyhedron /ˌpɒlɪˈhiːdɹən/, infinitesimal /ˌɪnfɪnɪˈtɛsɪməl/, flexibility /ˌflɛksɪˈbɪlɪti/

How to practise with this video

Listen to the whole video once without speaking and note the words you do not know.
Start at 0.75× speed, shadow it sentence by sentence, then go back to normal speed once it feels easy.
Record yourself and compare with the original, paying attention to words like polyhedron, infinitesimally, lengthen.

เทคนิค Shadowing คืออะไร?

Shadowing เป็นเทคนิคการเรียนรู้ภาษาที่ได้รับการรับรองทางวิทยาศาสตร์ พัฒนาขึ้นสำหรับการฝึกนักแปลมืออาชีพ วิธีการนี้เรียบง่ายแต่ทรงพลัง: คุณฟังเสียงภาษาอังกฤษจากเจ้าของภาษาและพูดตามทันที — เหมือนเงาที่ตามผู้พูดด้วยช่วงเวลาห่าง 1-2 วินาที การวิจัยแสดงว่าเทคนิคนี้ปรับปรุงความแม่นยำในการออกเสียง ทำนองเสียง จังหวะ การเชื่อมเสียง การฟังเข้าใจ และความคล่องแคล่วในการพูดได้อย่างมีนัยสำคัญ

เทคนิค shadowing: อ่านคู่มือฉบับเต็มทีละขั้นตอน →

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