We have seen how to obtain a line whose length is a rational number. How do we obtain lines whose lengths are irrational?
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Question

We have seen how to obtain a line whose length is a rational number. How do we obtain lines whose lengths are irrational?

KnowledgeBoat · Accepted Answer

To obtain a line segment of irrational length, we use the Baudhāyana–Pythagoras theorem and a geometric construction with ruler and compass. For example, to construct a line segment of length : Step 1 : Draw a line segment OA of length 1 unit. Step 2 : At point A, draw a perpendicular AB of length 1 unit. Step 3 : Join O to B. By the Pythagoras theorem : ⇒ OB2 = OA2 + AB2 ⇒ OB2 = 12 + 12 ⇒ OB2 = 2 ⇒ OB = . Step 4 : With O as centre and OB as radius, draw an arc cutting the number line at point P. Then OP = . This way, we can construct line segments of any irrational length of the form using the Pythagoras theorem repeatedly. Hence, we can obtain lines of irrational length by using right-angled triangles and applying the Pythagoras theorem.

Mathematics

We have seen how to obtain a line whose length is a rational number. How do we obtain lines whose lengths are irrational?

Whole Numbers

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