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Encapsulate
math

PlAyInG wITH COnSTRUCTIOnS

Curve

A shape or a line that is smoothly drawn in a plane having a bent or turns in it.
Circle Square

Set of points that are It is a two-dimensional closed shape
all at a fixed distance with 4 equal sides and each angle
(called radius) from measuring 90°.
a single point (called 2 cm O Construction:
centre) in a plane is 1. Draw a line segment AB.
called a circle. 2. Draw a perpendicular line on
Construction: point A of AB
1. Mark a point as O. 3. On the perpendicular, mark a point D such that
2. Take the required radius. AD = AB.
3. Keeping the pointer fixed at O, 4. Draw another perpendicular line at point B of AB
move the compasses slowly to and mark C on it, such that BC = AB = AD.
obtain the circle. 5. Join CD.
Rectangle

It is a two-dimensional Construct a rectangle where one of
closed shape with its sides is a cm and length of the
opposite side equal and diagonal is b cm.
each angle measuring 1. Draw the base AB of length
90°. ‘a’ cm.
Construction: 2. Draw a perpendicular at point B
1. Draw a line segment PQ. of AB.
2. Draw a perpendicular at point P. 3. Using a ruler, take a distance of ‘b’ cm in a
3. Mark a point S on the perpendicular. compass, and from A, mark an arc cutting
4. Draw another perpendicular at Q and perpendicular line at C. Join AC.
mark point R on the perpendicular such 4. Draw a perpendicular line at A on AB and cut
that PS = QR. AD = BC.
5. Join RS. 5. Join CD.

Construct a rectangle in which one of the diagonals divides the opposite angles in ∠a and ∠b.
1. Draw a line segment AB with an arbitrary length.
2. Draw a perpendicular BX on AB through B.
3. Put protractor at point A and make ∠BAC = ∠a, where point C lies on B.
4. Draw a line perpendicular to AB at A and mark the point D such that AE = BC.
5. Thus, ABCD is the required rectangle.

Knowledge Desk

To construct a square with area equal to the given circle using compass and ruler was one of the toughest
problem. Similarly, to construct a circle equal in area of square is not an easy task. Though Baudhayana had
dealt with these two problems in Sulba-Sutra.

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