A good baseball player takes 3 – 4 secs to run to 1st base.
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Posts Tagged ‘equation’
How MATH proves that Shakespeare is Your Ancestor!
February 20, 2024You have 2 parents, 4 grandparents, 8 great grandparents, ETC, ETC
The no. of ancestors you have per generation follows an EXPONENTIAL FUNCTION:
Here are the numbers going back 50 generations or 1,000 years.
When you plot YOUR NO. ANCESTORS over a POPULATION OF THE WORLD GRAPH there is a problem.
Population of the World DATA HERE
If you look at the graph (above) you will see that the No. YOUR ANCESTORS equalled the POPULATION OF THE WORLD about 500 years or 25 Generations ago.
You are related to everyone who was alive 500 years ago. Some of your ancestors inlcude:
Of course, EVERYONE else has these ancestors too.
If you go back 50 generations you have more ANCESTORS than the entire POPULATION OF THE WORLD.
Why?
Anthropologists say that there was a lot of IN BREEDING especially when humans lived in small tribes and the world population was small.
So way back every one of our family trees has members popping up all over the place. So we had far fewer ancestors than the math suggests.
I Can’t Sleep: Caffeine Math Part 3 USA UNITS
November 13, 2021I Can’t Sleep Math: Caffeine Maths METRIC HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
10 black teas
7 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
I Can’t Sleep: Caffeine Maths Part 3 METRIC
November 13, 2021I Can’t Sleep: Caffeine Math USA UNITS HERE.
Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology
Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.
Caffeine content sources Caffeine Content Data Base
Street art by JEKS, South Carolina
The Half life equation is an exponential function.
The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;
9 black teas
6 instant coffees
4 cappuccinos
2 dark roast brewed
less than one cup of Black Insomnia Coffee.
Approx half this amount of caffeine for 14 yos.
It is Xmas … Ah! The Joy of Algebra!
December 5, 2019
Great Math Xmas Ornament Ideas for Middle School here @ MathEqualsLove blog.
Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.
Can you escape a FALLING TREE?
August 24, 2019
Tragically, 5 people have been killed by falling trees in Victoria, Australia, this Winter.
In 3 separate accidents, 4 died when trees crushed the occupants in cars. One victim was a pedestrian.
So if you were walking through a park could you escape a falling tree if you either heard a cracking sound or saw the tree starting to fall?
With thanks to Physics Stack Exchange.
For an inverted pendulum near the top of its arc, there is no period, but the quantity √ℎ/𝑔 does represent a characteristic time scale for this system. The tree will take a few of these characteristic times to fall.
Mathspig hates seeing an old tree felled, but it does give us the necessary time data.
There are many assumptions in these calculations.
*You’d be hit by the tree trunk, not a branch which would hit you sooner.
*There is no wind pushing the tree over.
*The tree falling is an approx to a reverse pendulum.
The Equation that tried to break the internet!!!
August 3, 2019The following equation went viral on Twitter like the Yanni & Laurel sound Tweet. What answer do you get?
The Equation that tried to stump the internet! New York Times
And the tic tic toc of the HYPERBOLA CLOCK
May 19, 2019
This is why students HATE algebra
January 31, 2019
So Mathspig is helping the kid next door with Grade 11 Math.
Here is the revision Q:
This is the sort of Q that makes students hate ALGEBRA. (Solution by Mathspig below)
POINTLESS
GRINDING
HEADACHE INDUCING
This equation looks like a chicken ran through some ink and ran across the page.
Why do so many MATH work sheets look like this?
The result:
THE ALTERNATIVE
One way to tackle a long and complexmath problem is to defront the classroom and solve it in groups.
ALGEBRA Q from HELL SOLUTION
Here is the Q in orginal form:
NOTE: With a proof, you have to prove that one side of the equation
equals the other.
Simple Equation For Calculating Skyscraper Sway in an Earthquake
October 2, 2018A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.
This is intentional, as rigid structures can snap in strong winds or during earthquakes.
But the maths used to calculate SKYSCRAPER SWAY is straightforward.
The Earthquake Engineering website offers a simple explanation.
Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.
Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.
The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.
The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).
One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.
Earthquake Engineering
The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.
1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.
Details Base Isolation Specialists
2. Shock absorbers or dampers are added to the structure to dissipate the seismic shock.
Details Damper Supplier
3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.
The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly vomit inducing (barfomatic?).
The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.
It is pushed in the opposite direction to the building sway to dampen the oscillation.
Earthquake Engineering Maths
Take 1:
Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):
But I’m going to use a student friendly equation from Wind Engineering for Large Structures.
Calculus Equation here.
Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.
Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?
Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.
Mathspig Blog 