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A “standard-free” definition for the meter was actually proposed back in the 17th century. The Dutch mechanic, physicist, mathematician, astronomer, and inventor Christiaan Huygens suggested using a simple pendulum for this purpose. You...
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A “standard-free” definition for the meter was actually proposed back in the 17th century. The Dutch mechanic, physicist, mathematician, astronomer, and inventor Christiaan Huygens suggested using a simple pendulum for this purpose. You take a small object and suspend it on a string. The length of the string should be such that the pendulum completes a full oscillation (returns to its original position) in exactly two seconds. This length of string was called the “universal measure” or the “Catholic meter.” This length differed from the modern meter by about half a centimeter.
The proposal was well-received and adopted. However, problems soon arose. First, Huygens was dealing with what he called a “mathematical pendulum.” This is a “material point suspended on a weightless, inextensible string.” A material point and a weightless string are hardly the simple tools that every merchant would have on hand.
Second, it was quickly discovered that the length of the pendulum’s string varied in different parts of the Earth. Gravity cunningly decreased as one approached the equator and did not cooperate with humanity’s bright dream of standardization.
An astonishing equation
But let’s return to our mysterious equation. To find the period of small oscillations of a mathematical pendulum as a function of the length of the suspension, the following formula is used:
And here it is — our π! Let’s substitute the parameters of Huygens’ pendulum into this formula. The length of the string l in Huygens’ pendulum equals 1. The T — oscillation equals 2. Plugging these values into the formula, we get π²=g.
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<p id="7c74" class="pw-post-body-paragraph lh li fq lj b lk nd lm ln lo ne lq lr ls nf lu lv lw ng ly lz ma nh mc md me fj bk" data-selectable-paragraph="">A “standard-free” definition for the meter was actually proposed back in the 17th century. The Dutch mechanic, physicist, mathematician, astronomer, and inventor Christiaan Huygens suggested using a simple pendulum for this purpose. You take a small object and suspend it on a string. The length of the string should be such that the pendulum completes a full oscillation (returns to its original position) in exactly two seconds. This length of string was called the “universal measure” or the “Catholic meter.” This length differed from the modern meter by about half a centimeter.</p><p id="4ffd" class="pw-post-body-paragraph lh li fq lj b lk ll lm ln lo lp lq lr ls lt lu lv lw lx ly lz ma mb mc md me fj bk" data-selectable-paragraph="">The proposal was well-received and adopted. However, problems soon arose. First, Huygens was dealing with what he called a “mathematical pendulum.” This is a “material point suspended on a weightless, inextensible string.” A material point and a weightless string are hardly the simple tools that every merchant would have on hand.</p><p id="828f" class="pw-post-body-paragraph lh li fq lj b lk ll lm ln lo lp lq lr ls lt lu lv lw lx ly lz ma mb mc md me fj bk" data-selectable-paragraph="">Second, it was quickly discovered that the length of the pendulum’s string varied in different parts of the Earth. Gravity cunningly decreased as one approached the equator and did not cooperate with humanity’s bright dream of standardization.</p><h1 id="d7ed" class="mf mg fq bf mh mi mj mk ml mm mn mo mp mq mr ms mt mu mv mw mx my mz na nb nc bk" data-selectable-paragraph="">An astonishing equation</h1><p id="6a23" class="pw-post-body-paragraph lh li fq lj b lk nd lm ln lo ne lq lr ls nf lu lv lw ng ly lz ma nh mc md me fj bk" data-selectable-paragraph="">But let’s return to our mysterious equation. To find the period of small oscillations of a mathematical pendulum as a function of the length of the suspension, the following formula is used:</p><figure class="nl nm nn no np nq ni nj paragraph-image"><div class="ni nj nk"><picture><source srcset="https://miro.medium.com/v2/resize:fit:640/format:webp/0*Mt5zJi9B6SIuSmVV 640w, https://miro.medium.com/v2/resize:fit:720/format:webp/0*Mt5zJi9B6SIuSmVV 720w, https://miro.medium.com/v2/resize:fit:750/format:webp/0*Mt5zJi9B6SIuSmVV 750w, https://miro.medium.com/v2/resize:fit:786/format:webp/0*Mt5zJi9B6SIuSmVV 786w, https://miro.medium.com/v2/resize:fit:828/format:webp/0*Mt5zJi9B6SIuSmVV 828w, https://miro.medium.com/v2/resize:fit:1100/format:webp/0*Mt5zJi9B6SIuSmVV 1100w, https://miro.medium.com/v2/resize:fit:564/format:webp/0*Mt5zJi9B6SIuSmVV 564w" sizes="(min-resolution: 4dppx) and (max-width: 700px) 50vw, (-webkit-min-device-pixel-ratio: 4) and (max-width: 700px) 50vw, (min-resolution: 3dppx) and (max-width: 700px) 67vw, (-webkit-min-device-pixel-ratio: 3) and (max-width: 700px) 65vw, (min-resolution: 2.5dppx) and (max-width: 700px) 80vw, (-webkit-min-device-pixel-ratio: 2.5) and (max-width: 700px) 80vw, (min-resolution: 2dppx) and (max-width: 700px) 100vw, (-webkit-min-device-pixel-ratio: 2) and (max-width: 700px) 100vw, 282px" type="image/webp"><source data-testid="og" srcset="https://miro.medium.com/v2/resize:fit:640/0*Mt5zJi9B6SIuSmVV 640w, https://miro.medium.com/v2/resize:fit:720/0*Mt5zJi9B6SIuSmVV 720w, https://miro.medium.com/v2/resize:fit:750/0*Mt5zJi9B6SIuSmVV 750w, https://miro.medium.com/v2/resize:fit:786/0*Mt5zJi9B6SIuSmVV 786w, https://miro.medium.com/v2/resize:fit:828/0*Mt5zJi9B6SIuSmVV 828w, https://miro.medium.com/v2/resize:fit:1100/0*Mt5zJi9B6SIuSmVV 1100w, https://miro.medium.com/v2/resize:fit:564/0*Mt5zJi9B6SIuSmVV 564w" sizes="(min-resolution: 4dppx) and (max-width: 700px) 50vw, (-webkit-min-device-pixel-ratio: 4) and (max-width: 700px) 50vw, (min-resolution: 3dppx) and (max-width: 700px) 67vw, (-webkit-min-device-pixel-ratio: 3) and (max-width: 700px) 65vw, (min-resolution: 2.5dppx) and (max-width: 700px) 80vw, (-webkit-min-device-pixel-ratio: 2.5) and (max-width: 700px) 80vw, (min-resolution: 2dppx) and (max-width: 700px) 100vw, (-webkit-min-device-pixel-ratio: 2) and (max-width: 700px) 100vw, 282px"><img alt="" class="bh kp nr c" width="282" height="122" loading="lazy" role="presentation" src="https://miro.medium.com/v2/resize:fit:564/0*Mt5zJi9B6SIuSmVV"></picture></div></figure><p id="b747" class="pw-post-body-paragraph lh li fq lj b lk ll lm ln lo lp lq lr ls lt lu lv lw lx ly lz ma mb mc md me fj bk" data-selectable-paragraph="">And here it is — our π! Let’s substitute the parameters of Huygens’ pendulum into this formula. The length of the string l in Huygens’ pendulum equals 1. The T — oscillation equals 2. Plugging these values into the formula, we get π²=g.</p><p id="3aee" class="pw-post-body-paragraph lh li fq lj b lk ll lm ln lo lp lq lr ls lt lu lv lw lx ly lz ma mb mc md me fj bk" data-selectable-paragraph=""></p> |
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