Skip to main content

Shape and Space

Transforming shapes

Reflection: With reflection the object and its image are congruent because they are the same size and shape.

Rotation: You need three things to describe a rotation: (a) the centre (b) the angle (c) the direction (e.g. clockwise).

Enlargement: The scale factor of an enlargement can be found by dividing corresponding lengths on two pictures.

Reduction: Even though a shape has undergone a reduction, mathematicians prefer to call it an enlargement with a fractional scale factor.

Translation: A translation is simply a 'shift'. There is no turning or reflection and the object stays the same size. Translations are described by vector. In a vector the top number gives the number of units across (positive to the right) and the bottom number gives the number of units up/down (positive upwards).

Translation with a vector

Tessellations: A tessellation is formed when a shape (or shapes) fit together without gaps to cover a surface, like jigsaw puzzles to cover a plane.

Bearings: are used where there are no roads to guide the way. Ships, aircraft and mountaineers use bearings to work out where they are. Bearings are measured clockwise from North. The bearing of A from B is the direction in which you travel to get to A from B.

Locus: In mathematics, the word locus describes the position of points which obey a certain rule. The locus can be the path traced out by a moving point.

Three important loci:

(a) Circle: The locus of points are equidistant from a fixed point O, it is a circle with centre O.
(b) Perpendicular bisector: The locus of points are equidistant from two fixed points A and B. It is the perpendicular bisector of the line AB. You can use compasses to draw arcs, or use a ruler and a protractor.
(c) Angle bisector: The locus of points are equidistant from two fixed lines AB and AC. It is the line which bisects the angle BAC. You may use compasses to draw arcs or use a protractor to construct the locus.

Pythagoras' theorem:
Pythagoras (569 - 500 BC) was one of the first of the great mathematical names in Greek antiquity. He settled in southern Italy an formed a mysterious brotherhood with his students who were bound by an oath not to reveal the secrets of numbers and who exercised great influence. They laid the foundations of arithmetic through geometry and were among the first mathematicians to develop the idea of proof.


Popular posts from this blog

Does pearls reproduce by itself through time

At the request of several families he and Mrs Legge gave a home for some months to a young Dutch girl, a granddaughter of the first Dutch governor of the Straits Settlements. She had several pearls of which the Dutch residents were great collectors, got from oysters found in a river of the Malay Peninsula, when she left them she gave Mrs Legge a small box containing a large pearl the size of a pea, with a blue spot on it, and two others not so large. This box was then put away and locked up. Several weeks later he took it out and on opening it discovered more than a dozen pearls, most of them very small. Astonished at the phenomenon he called his chief servant, a Portuguese, who happened to enter the room and who expressed no surprise but declared it to be a common occurrence. On enquiry he found that many of the Dutch people had jars of pearls, large and small, which had accumulated in this way. Some years later he related the incident at dinner on board ship. The captain was a cautio

Bidmas, Bedmas, Bodmas, Pedmas And Christmas

This BBC GCSE Bitesize post says, BODMAS stands for 'brackets', 'other', 'division', 'multiplication', 'addition' and 'subtraction'. It's the order in which we carry out a calculation. But another article says, the order of operations in Maths called BIDMAS. BIDMAS stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. The difference is that the second substitute 'o' with 'i', and we can understand that teacher normally chooses easy way to explain whose pupils can understand, exponent or power or indices are out of reach of foundation students, so teachers uses 'other' instead. And in this article , 'o' actually stands for 'order', as far as my memory can go, my English teacher never teach me 'order' actually means 'Powers and Square Roots, etc.' In United States, the mnemonic fo Order of Operation is PEMDAS, because brackets are called pa

Panic or panick

There is only one spelling for panic ; the verb is inflected 'panic, panics, panicked, and panicking’. The form panick is used for progressive tense, past tense and past participle. We don't write panick today, though English speakers from a few hundred years ago might have (in the same way they might have written musick). When the alternate spelling “panick” is used for the past participle: "I panicked last night at the disco." When it’s use for progressive tense: “Invariably, when markets are panicking, they sell the stocks quickly.” It's the rule for root words ending in "c" is that you have to add “k”, so the spelling is related with the pronunciation. If we don't add the <k>, it looks as if the <c> has to be pronounced /s/. If the "k" was not there, “panicing” would look like the word which is supposed to be pronounced as if it is ended in "sing," while “paniced” would be pronounced like “panised”. The same