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.



Labels:

Comments

Post a Comment

Popular posts from this blog

Nightsoil men

In Victorian time, building were often put up before water and sewage pipes were laid down so a single tap or pump might have to serve hundreds of people. Toilet waste was carried away by 'nightsoil men'.  Some seeped into the water supply and rivers became polluted by factory and human waste. In 1858, the Thames in London became so smelly that the year was known as 'the year of the Great Stink'!
Post a Comment
Read more

The Indian Mutiny

British rulers were shaken to the core by the Indian Mutiny of 1857. The spark which lit the fuse of the rebellion was when cartridges were given to Indian troops which were coated in grease, made from cow or pig fat. These cartridges had to be prepared for firing by being bitten at one end. The cow is a sacred animal to the Hindus and the pig is regarded as unclean by Muslims, so no one was happy. Indian troops refused to bite the cartridges. Their British officers hanged a few. The troops rioted. They killed their officers, ransacked Delhi, and massacred British men, women and children. For a long time it looked as if the British might be defeated. The rebellion was about more than just biting cartridges. It was a revolt against taxation and the laws of the East India Company, which ruled India for Britain. After the mutiny, the British were a lot more careful about how they governed India. When the news of the mutiny reached England, crowds bayed for blood and Victoria was hor...
Post a Comment
Read more

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 ...
1 comment
Read more