Sounds like a top tapper
QUESTION During tap dancing sequences in old Hollywood musicals, do we hear the actual taps made by the dancer or are they dubbed later?
The tapping was usually dubbed after the performance. The actor/dancer would go to a Foley studio and record a tap track on a wooden floor to match the image on the screen for a cleaner sound.
Most top-rank dancers didn’t do their own Foley work, and dancers who stood in were usually uncredited.
Two major exceptions were Fred Astaire and eleanor Powell. According to John Mueller, author of Astaire Dancing: ‘Astaire insisted on dubbing all his own taps. hermes Pan tended to dub Ginger Rogers’s taps, so you’re hearing hermes Pan, but you’re seeing her dance.’ hermes Pan (Panagiotopoulos) was Fred Astaire’s choreography partner.
eleanor Powell (1912-82), the star of hollywood extravaganzas such as Born To Dance (1936), Broadway Melody Of 1938 and Rosalie ( both 1937), also overdubbed herself to ensure her signature crispness of sound. It also allowed her to wear more attractive shoes on screen.
One film in which the singing and tapping was recorded live on the soundstage was Roberta (1935). In the dance to I’ll Be hard To handle, you can hear Ginger Rogers giggling with joy as she is whirled around.
Audrey Wisher, Bath, Somerset.
QUESTION Are there any countries that have land borders, but drive on different sides of the road?
ThAnks, in main, to the British empire, much of the world, including the U.s., drove their carriages and cars on the left until the early 19th century, with parts of Canada doing so into the early 20th century. Most countries have since joined the right-hand-side (Rhs) club.
some of the remaining major left-hand- side (Lhs) countries (Britain, Japan, Australia and new Zealand) are islands, but exceptions include the countries of south-east Africa and the nations that were once British India.
While many of these border one another, inevitably some have a land border with countries that drive on the opposite side of the road.
namibia (Lhs) borders Angola (Rhs); Zambia (Lhs) borders the Democratic Republic of the Congo (Rhs) and Angola (Rhs); Uganda (Lhs) borders Rwanda, south sudan and DR Congo, which all drive on the right.
Pakistan (Lhs) shares borders with Afghanistan, China and Iran, which drive on the right. Thailand drives on the left, but three of its neighbours, Cambodia, Laos and Myanmar, drive on the right.
Usually these borders just use a traffic light to alternate the flow of vehicles.
Like hong kong, Macau still drives on the left under Chinese rule, which means travellers between Macau and other parts of China must switch sides of the road without leaving the country.
To ensure a smooth flow of traffic, the Lotus Bridge was built connecting Macau and hengqin Island, allowing traffic to travel unimpeded between left-hand Macau and right-hand China.
Completed in 1999, it is a fantastically elaborate construction, featuring three lanes in each direction and dual bridges that loop around each other by 360 degrees to swap the direction of the traffic without drivers needing to stop their vehicles.
Leonard Caine, Bewdley, Worcs.
QUESTION Other than maths teachers, which occupations use algebra?
As A maths teacher with 25 years’ experience, this is a common question asked by students: how can a jumble of letters help me in a future career, they ask? The answer is that the letters represent real values, but until the values are calculated, they remain variables. For example, when we design weapons or equipment for the military, we have to build models of how the weapon is going to behave in real life.
so we allow the time into the launch to be represented as t, say, velocity as v and the height as h. The position, bearing and other variables assume other letters.
For each value of t, the other values are calculated by using formulae we believe reflect reality. These techniques are necessary because we wish to minimise the costs of developing the weapon — it is extremely expensive to fire a gun or missile to test its performance, but cheap to model performance in a lab.
As another example, life assurance uses algebra to calculate premiums and pensions. A person with a pension pot might wish to buy an annuity.
Variables in the various formulae include the expected rate of interest received from the pension pot during the receiver’s lifetime, the rate of interest given to the receiver and the probability of them living in successive years to receive the annuity.
As students continue to study mathematics into sixth form, they learn advanced techniques such as integration to help them solve real-life problems.
Ian Hay, Sandy, Beds. ALGeBRA is the formal way of solving equations to find the values of unknown quantities. nowadays this is routinely done by specialist software, but spreadsheets make data processing accessible to anyone. spreadsheet formulas are equations within which functions derive new information.
Ken Warren, Sidmouth, Devon.