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### The Eureka moments of my household

How could my toilet and the famous Greek mathematician, Archimedes, be in the same story? The former one was made in US in 1976 and the latter one lived around 250 BC, but the stories of his eccentric geeky behaviour and brilliant sparks of mind are told and re-told all around the world even in our days. In one of such stories, he jumped out of a bathtub, naked, and run around the city overwhelmed with joy screaming "Eureka!" that means "I have found it!" when he discovered how to help the king verify that his wreath is made entirely of gold. The king ordered a golden crown to be made in the shape of a laurel wreath, but was not certain whether all the gold given to the goldsmith was put to use. The weight of the wreath was equal to the weight of the assigned gold, but what if a part of gold was replaced with some other metal? King asked the master mathematician for his help. Even back then, in 3rd century BC, the best ideas were coming to people in a shower or a bathtub. When Archimedes immersed himself in the tub and saw the water going up, he realized that the volume of the water that gets pushed out is equal to the volume of the object that is being put in. Therefore, he could immerse the king's wreath into the water to measure the volume of this complex object. Volume is equal mass times density. The mass of the gold assigned for the crown was known, as well as density of gold. So, if equation stands for measured numbers, then wreath is pure gold. If equation breaks, then part of gold has been replaced with other metal of the same weight but different density. Thrilled with this discovery, Archimedes run out of the bathtub right to the king, naked...

You see - math is hiding in every single room of our households, including even bathrooms and toilets. Why does the water go up when you are desperately trying to push the plunger? Although a plunger is as far from the golden wreath as any object could be, it similarly pushes away the water proportionally to its volume as Archimedes discovered during his Eureka moment in the bathtub. It is interesting that it does not really matter what is your plunger made of, metal or resin plunger would push out the same amount of water if plungers are of the same size and shape. But buying this new orange UFO-shaped plunger at the museum store was not necessarily a good idea. Mere immersion of it into my toilet has caused a serious flooding. Some things belong to the museum.

Now follow me to the basement where the washer and dryer are. This is where a little math has made one of the most strategic breakthroughs of my household. After a year of weekly laundry routine and the occasional mid-night crisis wash, we were looking for the bottleneck. The answer began with a simple question: “What is the first item that we run out of?” Not very sophisticated analytical investigation pinpointed that our laundry demands have been dictated by the lack of clean underwear. A trip to the store and \$50 has allowed us to run half of the washing cycles per month. This has saved plenty of detergent, lowered our gas bills and most importantly allowed us to watch one more movie each week.

Try more stories about cool math of home ownership: How Patrick Dempsey and HDTV may be responsible for obesity or The House Hunting Story.

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