This exercise works best if for homework the middle school students count the digits in their own cell phone, passport, bill code or some other number. They don’t have to show the passport or bill. They just have to count the digits.
Albert Digital Mathematical clocks are fascinating.
You calculate the time using +, -, x and ÷ . Such fun and ideal for the math classroom.
Mathspig found the Albert Mathematical clock at the Horsham International Hotel (below).
More info on the Albert Digital Clock here.
You can set the level of difficulty. You get 1 minute to work out the answer and that’s long enough.
………………………………………..Ben Zauzmer, a Harvard Applied Math graduate who has a 75 per cent success rate in predicting the winners of Oscar Awards every year, has correctly predicted 20 of 21 winners in 2018 Oscars, which is a success rate of 95%.
How does he do it? He gathers thousands of data points on Oscar ceremonies over the past two decades – such as categories movies are nominated in, other award results, and aggregate critic scores – and he uses statistics to calculate how good a predictor each of those metrics is in each Oscar category. Then, he plugs in the numbers and that gives him the % chance that each film will win in each category according to the Boston Globe.
Ben, who writes for The Hollywood Reporter, uses his mathematical model to produce Bar Graphs like this:
This year the Best Picture was a close call, but Ben’s Mathematical Prediciton was correct.
According to the fab NBC video, Mathletes, nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.
Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018
Kailani Craine, Australia
This is a typical figure skating score card for one competitor.
The final score, however, is based on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.
Screen grab NBC Mathletes
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)
Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.
The average:
Same score cards but Skater B gets a higher average score than Skater A.
Skater A is, in fact, beaten by a random number selector!!!!
While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.
The significant maths for ski jumpers is therefore X-section area.
Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!
A ski jumper is set to jump in Pyeongchang.
Casey Larson USA Pyeong chang 2018
Ski jumpers increase their speed going down the ramp by reducing their X-section area:
Lindsey Van, USA, practicing in a wind tunnel
Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum angle.
Abby Hughes, USA, practicing in a wind tunnel.
Abby Hughes, USA, in the air
Here is the formula for Air Resistance of Drag:
D = ½CApv2
Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.
A is the X-section Area,
p is the density of the air and
v the velocity of the object.
More here.
As Abby Hughes has tripled here X-section area in the air she will have tripled the vertical drag during her jump. This will slow here decent.
*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.
Here is the sensational pairs team from the 2018 Winter Olympics.
But why do ice skaters spin so fast?
Here is the math!
Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.
L = angular momentum
v = linear velocity
r = separation of object
Louisa Barama, USA
Let’s have a look at this equation:
The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.
Other spins include:
Mao Asada, Japan, triple Axel
……………………………………………………………………………………………..
Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.
To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:
…………………………………………………………………………………
More info here.
Kim Yuna, South Korea
Now, mathspiggies, you must separate Linear Velocity (v1 ) from Angular Velocity (vr ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.
But when that same foot is in a Triple Axel postion it moves in a very, very small circle.
Patrick Chan, Canada, Camel Spin
Patrick Chan, Canada, Triple Axel
By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.
Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.
Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.
Look at the numbers:
…………………………………………………………………………………
That’s about right.
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