20201016 (Friday / viernes)

12

Marathon, 26 miles 385 yards

How to convert the marathon distance from the Anglo-Saxon system of measurements to the decimal metric system: 26 miles 385 yards, to kilometers (or meters)

Such distance was set during the Games of the IV Olympiad in London 1908 (the king was Edward VII, of the House of Saxe-Coburg and Gotha, and his wife was the queen consort Alexandra of Denmark, while the Prime Minister of the United Kingdom was the liberal Herbert Henry Asquith).

One mile equals 1.609344 kilometers.

A clarification: we must NOT multiply 26.385 by 1.609344, since the Anglo-Saxon system is NOT decimal, but it is necessary to separate the different Anglo-Saxon units of measurement.

First, let's take the 26 miles and multiply them by 1.609344:

26 × 1.609344 = 41.842944 kilometers,

which are equivalent to 41,842.944 meters.

Now, let's take the 385 yards and convert them to kilometers.

First, we will convert them to meters.

One yard equals 0.9144 meters.

Let's multiply 385 by 0.9144:

385 × 0.9144 = 352.044 meters.

Now, let's convert 352.044 meters to kilometers.

One kilometer equals 1000 meters.

Let's divide by 1000:

352.044 / 1000 = 0.352044

0.352044 kilometers.

We must add these 0.352044 kilometers to the figure that we had obtained in our first operation (41.842944 kilometers):

41.842944 + 0.352044 = 42.194988 kilometers

which are equivalent to 42,194.988 meters which, when rounded, are 42,195 meters (forty-two thousand one hundred ninety-five meters).

It is affirmed, then, that:

The marathon event is therefore 42.195 kilometers long (42 kilometers and 195 meters).

[The distance set in London for the marathon event actually fell short of 42,195 meters, by 0.012 meters, that is, by 1.2 centimeters —less than half an inch—. Please remember this bracketed paragraph and this 1.2 cm figure, as we will return to them at the end of this text.]

Now, let's suppose something that did NOT happen: that in the Games of the I Olympiad in Athens 1896, the EXACT distance had been set at 42,195 meters, and an inhabitant of the Anglosphere wanted to know its equivalence in miles, yards, feet, and inches.

We take 42,195 meters and divide them by the value of a mile expressed in meters (1,609.344):

42,195 / 1,609.344 = 26.2187574564543

We have 26 miles and change.

For now, let's subtract 26:

26.2187574564543 - 26 = 0.2187574564543

These 0.2187574564543 decimals of a mile must be converted to yards.

A mile equals 1760 yards.

So we multiply:

0.2187574564543 × 1760 = 385.01312336 yards.

We have 385 yards and change.

And if we subtract 385:

385.01312336 - 385 = 0.01312336

Now we have 0.01312336 decimals of a yard.

A yard is exactly three feet.

If we multiply that figure of 0.01312336 by 3, we will have:

0.01312336 × 3 = 0.03937008 feet.

Bu-u-ut, since we have not obtained even a full foot, but less than a twenty-fifth part of a foot, let's say this last arithmetic operation has not been carried out, and let's jump to inches.

One yard equals 3 feet, and it also equals 36 inches (one foot equals 12 inches).

So those decimals of a yard that we have, we must multiply them by 36:

0.01312336 × 36 = 0.47244096 inches.

We get a little less than half an inch.

Our answer is:

26 miles, 385 yards, 0 feet, and 0.47244096 inches.

— —

Now, if we want to know the equivalence of those 0.47244096 decimals of an inch, in the metric decimal system, we must multiply them by the value of an inch in the mentioned metric decimal system, which is 2.54 centimeters:

0.47244096 × 2.54 = 1.2

1.2 centimeters

... which is equal to the difference indicated above, in between brackets.

— —

Maratón, 42.195 kilómetros

Cómo convertir la distancia del maratón desde el sistema anglosajón de medidas al sistema métrico decimal: 26 millas 385 yardas, a kilómetros (o a metros)

Tal distancia fue fijada durante los Juegos de la IV Olimpiada de Londres 1908 (los reyes eran Eduardo VII [Edward VII], de la Casa de Sajonia-Coburgo y Gotha [House of Saxe-Coburg and Gotha] y su esposa Alejandra de Dinamarca [Alexandra of Denmark]), y el primer ministro del Reino Unido era el liberal Herbert Henry Asquith).

Una milla equivale a 1.609344 kilómetros.

Una aclaración: NO se debe multiplicar 26.385 × 1.609344, ya que el sistema anglosajón NO es decimal, sino que es necesario separar las distintas unidades anglosajonas de medida.

Primeramente, tomemos las 26 millas y multipliquémoslas por 1.609344:

26 × 1.609344 = 41.842944 kilómetros,

que equivalen a 41,842.944 metros.

Ahora, tomemos las 385 yardas y convirtámoslas a kilómetros.

Primeramente, las convertiremos a metros.

Una yarda equivale a 0.9144 metros.

Multipliquemos 385 por 0.9144:
385 × 0.9144 = 352.044 metros.

Ahora, convirtamos 352.044 metros a kilómetros.

Un kilómetro equivale a 1000 metros.

Dividamos entre 1000:
352.044 / 1000 = 0.352044

0.352044 kilómetros.

Debemos sumar estos 0.352044 kilómetros a la cifra que habíamos obtenido en nuestra primera operación (41.842944 kilómetros):

41.842944 + 0.352044 = 42.194988 kilómetros

que equivalen a 42,194.988 metros que, redondeados, son 42,195 metros (cuarenta y dos mil ciento noventa y cinco metros).

Se afirma, entonces, que:

La prueba maratón tiene, pues, una longitud de 42.195 kilómetros (42 kilómetros y 195 metros).

[La distancia fijada en Londres para la prueba maratón en realidad se quedó corta para los 42,195 metros, por 0.012 metros, o sea, por 1.2 centímetros. Recordemos este párrafo encorchetado y esta cifra de 1.2 cm, pues volveremos a ellos al final de este texto.]

Ahora bien, supongamos algo que NO sucedió: que en los Juegos de la I Olimpiada de Atenas 1896, la distancia EXACTA hubiera sido fijada en 42,195 metros, y un habitante de la angloesfera quisiese saber su equivalencia en millas, yardas, pies y pulgadas.

Tomamos 42,195 metros y los dividimos entre el valor de una milla expresado en metros (1,609.344):

42,195 / 1,609.344 = 26.2187574564543

Tenemos 26 millas y algo más.

De momento, restemos 26:

26.2187574564543 - 26 = 0.2187574564543

Estos 0.2187574564543 decimales de milla debemos convertirlos a yardas.

Una milla tiene 1760 yardas, o equivale a 1760 yardas.

Así que multiplicamos:
0.2187574564543 × 1760 =
385.01312336 yardas.

Tenemos 385 yardas y algo más.

Y si restamos 385:
385.01312336 - 385 = 0.01312336

Ahora tenemos 0.01312336 decimales de yarda.

Una yarda tiene exactamente tres pies, o equivale a tres pies exactamente.

Si multiplicamos por 3 esa cifra de 0.01312336, tendremos:
0.01312336 × 3 = 0.03937008 pies.

Peeero, como no hemos obtenido ni siquiera un pie completo, sino menos de la vigésima quinta parte de un pie, demos por no efectuada esta última operación aritmética, y saltemos a las pulgadas.

Una yarda equivale a 3 pies, y también equivale a 36 pulgadas (un pie equivale a 12 pulgadas).

Así que aquellos decimales de yarda que tenemos, debemos multiplicarlos por 36:

0.01312336 × 36 = 0.47244096 pulgadas.

Obtenemos un poco menos de media pulgada.

Nuestra respuesta es:

26 millas 385 yardas 0 pies y 0.47244096 pulgadas.

— —

Ahora, si queremos saber la equivalencia de esos 0.47244096 decimales de pulgada, en el sistema métrico decimal, debemos multiplicarlos por el valor de una pulgada en el mencionado sistema métrico decimal, que es de 2.54 centímetros:

0.47244096 × 2.54 = 1.2

1.2 centímetros

... que es igual a la diferencia arriba señalada, entre corchetes.

20201016 (Friday / viernes)