From Zero To Infinity (And Beyond)

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With this book, children can unlock the mysteries of maths and discover the wonder of numbers. Readers will discover incredible information, such as why zero is so useful; what a googol really is; why music, maths and space are connected; why bees prefer hexagons; how to tell the time on other planets; and much much more.

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From marvellous measurements and startling shapes, to terrific theories and numbers in nature — maths has never been as amazing as this! Dr Mike Goldsmith holds a PhD in astrophysics from Keele University, and has written 40 books on a range of scientific topics for children and adults.

Dr. Neil Turok - From zero to infinity, and beyond!

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'From zero to infinity'

Find us elsewhere online. Look inside. When light passes through water, for example, its phase velocity is reduced as its wavelengths get squished together. Once it exits the water, its phase velocity increases again as its wavelength elongates.

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How much the crests of a light wave slow down in a material is expressed as a ratio called the refraction index — the higher the index, the more the material interferes with the propagation of the wave crests of light. Water, for example, has a refraction index of about 1.

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When the refraction index is reduced to zero, really weird and interesting things start to happen. In a zero-index material, there is no phase advance, meaning light no longer behaves as a moving wave, traveling through space in a series of crests and troughs. Instead, the zero-index material creates a constant phase — all crests or all troughs — stretching out in infinitely long wavelengths.

The crests and troughs oscillate only as a variable of time, not space. This uniform phase allows the light to be stretched or squished, twisted or turned, without losing energy. A zero-index material that fits on a chip could have exciting applications, especially in the world of quantum computing. The metamaterial consists of silicon pillar arrays embedded in a polymer matrix and clad in gold film.