sharesgaq.blogg.se - Triangle with circle outside

Rather than construction, the shapes could be drawn by working out the lengths using Pythagoras’ Theorem. Is there a way?ĭownload my worked example of the construction of the Alchemist symbol. I cannot see a way to construct the symbol starting with the outside circle. They meet at the centre of the large circle.Join the midpoints to the opposite corners to construct the medians.Bisect the three sides of the large equilateral triangle.Extend the small equilateral triangle until it reaches the extended base.

Extend the base of the square either side.

Construct an equilateral triangle on the top of the square.

Draw in the diagonals to find the centre for the smaller circle.

A 5 cm square in the centre of an A4 sheet of paper works nicely, in that the final shape will fit on the paper.

Construct a square of given length by constructing a right angle at the end of a line segment.

The key is to start with the square and work from there. The complete symbol can actually be constructed using only basic constructions present in the GCSE syllabus. The same method would work to prove the circle centres are not concurrent. This could be disproved formally for higher ability students, or if a drawing of the symbol was given to the students a little exercise in transformations using tracing paper would show this to be false.

There are some dangerous misconceptions to iron out first – for example, the belief that the top corners of the square lie at the midpoints of the sides of the equilateral triangle. Even a vocabulary test of ‘name the shapes that you see’ (or ‘identify the following’) would generate: circle, equilateral triangle, isosceles triangle, square, segment, chord and trapezium. The questions could range from something as open as ‘Do some maths with that’ to a more specific ‘What is the ratio of the circumferences of the two circles?’, or ‘Prove that the circles do not have the same centre’. The symbol could be presented to students of almost any level of ability. The sign above the door and on their business cards caught my interest. Visiting my home town of Leeds recently, my relatives took me to a restaurant in the city centre called The Alchemist.