The universe is big, but it’s peanuts compared to the eternally inflating multiverse. But just how many universes are there? What are they like? And most importantly, what can they tell us about … aliens?

Imagine it: the observable...

Our universe started with the big bang. But only for the right definition of “our universe”. And of “started” for that matter. In fact, probably the Big Bang is nothing like what you were taught.

A hundred years ago we discovered...

Scientists at the Large Hadron Collider may have just discovered a new fundamental particle that could change the way we look at the universe. Is this Dark Energy? A giant Neutrino? The big brother of the Higgs Boson? Or could it be the...

Space is big, and it’s getting bigger. But where does all that new space actually come from? And is it popping into existence all around you right now? Is that why the remote control is always further away than I thought?

We've come a long way in our understanding of dark energy. In previous episodes we've looked at how our universe is paradoxically flat and how dark energy is exponentially accelerating the expansion of the universe. Now, let's dive into...

Pupil outcome: You can identify and describe the relationship between two regular polygons using scale factors Key learning points: - Two similar shapes can be described as being 'x' times greater or smaller than each other. - If one...

Pupil outcome: I can enlarge objects using information about the centre of enlargement and scale factor Key learning points: - Each length in the shape is multiplied by the scale factor - Each vertex in the object is a given distance...

Pupil outcome: I can draw an accurate scaled diagram using a suitable choice of scale. Key learning points: - Given the real measurements, a suitable scale factor can be chosen. - The scale factor should mean the scaled diagram is easy...

Pupil outcome: I can use my knowledge of similarity to solve problems. Key learning points: - A scaled version of a shape is very useful. - Being able to scale the perimeter can reduce the number of calculations. - Enlargement...

Pupil outcome: I can understand the effect of an enlargement on the volume of a 3D shape. Key learning points: - An enlargement means the object and image are similar. - All lengths in the object have been multiplied by the scale factor....

Pupil outcome: I can describe an enlargement and perform a given enlargement on an object. Key learning points: - Each length in the shape is multiplied by the scale factor. - Each vertex in the object is a given distance from the centre...

Pupil outcome: I can perform a given enlargement on an object. Key learning points: - Each length in the shape is multiplied by the scale factor. - Each vertex in the object is a given distance from the centre of enlargement. - This...

Pupil outcome: I can describe an enlargement and perform a given enlargement on an object. Key learning points: - Each length in the shape is multiplied by the scale factor. - Each vertex in the object is a given distance from the centre...

Pupil outcome: I can describe an enlargement. Key learning points: - If the image is the opposite side of the centre of enlargement and rotated 180°, there is a negative scale factor. - If the image has changed size, there has been an...

Pupil outcome: I can calculate the scale factor used to enlarge a volume and use it to find missing lengths. Key learning points: - You can calculate the scale factor from the two volumes. - Having calculated the scale factor, you can...

Pupil outcome: I can understand the effect of an enlargement on the area of a shape. Key learning points: - An enlargement means the object and image are similar. - All lengths in the object have been multiplied by the scale factor. -...

Pupil outcome: I can describe the relationship between scale factors and side lengths and perimeters of two shapes. Key learning points: - If the lengths of the sides of a shape have been doubled, the perimeter will be double. - If the...

Pupil outcome: I can calculate the scale factor used to enlarge an area and use it to find missing lengths. Key learning points: - You can calculate the scale factor from the two areas. - Having calculated the scale factor, you can find...

Pupil outcome: I can understand the effect of an enlargement on the perimeter of a shape. Key learning points: - An enlargement means the object and image are similar. - All lengths in the object have been multiplied by the scale factor....

Pupil outcome: I can understand the minimum information required to describe an enlargement Key learning points: - The scale factor is the multiplier. - The centre of enlargement defines where the image will be placed in relation to the...

Pupil outcome: I can use my knowledge of similarity to solve problems. Key learning points: - A scaled version of a shape/object is very useful. - Being able to scale the perimeter/area/volume can reduce the number of calculations. -...

Pupil outcome: I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved. Key learning points: - An enlargement means a change in size. - The lengths of the lines may change when enlarged. -...

Pupil outcome: I can enlarge a shape and can state what changes and what is invariant. Key learning points: - An enlargement means a change in size. - The lengths of the lines may change when enlarged. - The angles inside an object do...

In this video, we will dilate figures on the coordinate plane when the center of dilation is not the origin. The first example is a standard dilation (enlargement) with a non-origin center, and the second example gives you both the...