Counting 1+2+3+…+n and Inscribed/Circumscribed Circles Within an Equilateral Triangle

Yes, we are doing math! After Science, then a little bit Science and History, then English, now we have some math t0 do! Okay, if that title made zero sense to you, well you’re not alone. Math may seem hard, confusing, and ridiculous at first, but eventually you’ll get the gist of it.

Okay! First, counting 1+2+3+…+n super quickly. In that statement, “…” means basically all the numbers between (in this case) 3 and n. So for example, you could have 1+2+3+4+5+6, where in this formula, the n equals 6.

Oh, we haven’t gotten to the formula yet? Here it is:

That’s a sigma symbol, which I won’t explain today, but I kinda understand.

yes I know it looks really confusing but the point is this, 1+2+3+…+n is always n(n+1) divided by 2. So, if like in our previous example, n=6, it’ll be 6 * 7 / 2. Which is 21, and if you try to check it using the normal boring slow method, it’ll be correct.

This will work with any value of n, so if you would like to know 1+2+3+…+98+99+100, you know it’ll be 100 * 101 / 2, which is is 5050. Not really that hard when you’ve got the formula right?

Okay, next one! This one’s a little bit harder but the key is always logic, and most of the time requires a formula. Here we go! Imagine three equal-sized circles inscribed/circumscribed/tightly packed into an equilateral triangle. Each of the circle has a radius of 1 cm. Now, try to find the perimeter of this triangle:

So, let’s start by first making a small triangle at the corner:

Cool!

Okay, so how did I find these angles? Simple. The bigger triangle is equilateral, so each angle is 60°, and now we’ve halved it. 30°. Next how did I get the 60°? Obviously the other angle is a right angle (90°), so then 180-30-90=60°. Understand so far?

Alright, now we reach the formula part. For every 30-60-90 triangle, there’s a formula to find out their sides:

Yes, there’s a formula for everything!

So well yeah. Just put in the radius, which is 1 in this case, into a, and boom. We’ve got all the side lengths. The rest is easy.

So yeah. The rest of the side is just the radii of the circle, 1 cm each, so for every side it’s 2 + 2 √3 cm and so for the perimeter, it’s just (2 + 2 √3 cm) * 3 = 6 + 6 √3 cm!

Okay, so today we finished two pretty hard-looking but essentially easy enough (with the formula) questions. How did you feel about this week’s Weekend Lessons? Leave your comments below and have a good day!

Benjamin Zephaniah’s Talking Turkeys – An Analysis

Talking Turkeys

Be nice to yu turkeys dis christmas
Cos’ turkeys just wanna hav fun
Turkeys are cool, turkeys are wicked
An every turkey has a Mum.
Be nice to yu turkeys dis christmas,
Don’t eat it, keep it alive,
It could be yu mate, an not on your plate
Say, Yo! Turkey I’m on your side.
I got lots of friends who are turkeys
An all of dem fear christmas time,
Dey wanna enjoy it, dey say humans destroyed it
An humans are out of dere mind,
Yeah, I got lots of friends who are turkeys
Dey all hav a right to a life,
Not to be caged up an genetically made up
By any farmer an his wife.

Turkeys just wanna play reggae
Turkeys just wanna hip-hop
Can yu imagine a nice young turkey saying,
‘I cannot wait for de chop’,
Turkeys like getting presents, dey wanna watch christmas TV,
Turkeys hav brains an turkeys feel pain
In many ways like yu an me.

I once knew a turkey called…Turkey
He said “Benji explain to me please,
Who put de turkey in christmas
An what happens to christmas trees?”,
I said “I am not too sure turkey
But itÕs nothing to do wid Christ Mass
Humans get greedy an waste more dan need be
An business men mek loadsa cash’.

Be nice to yu turkey dis christmas
Invite dem indoors fe sum greens
Let dem eat cake an let dem partake
In a plate of organic grown beans,
Be nice to yu turkey dis christmas
An spare dem de cut of de knife,
Join Turkeys United an dey’ll be delighted
An yu will mek new friends ‘FOR LIFE’.

Benjamin Zephaniah

Yup. It’s time for poems. Today I’ll take a look at Talking Turkeys by Benjamin Zephaniah, and analyse it.

  • Title
    • Talking Turkeys can be an informal phrase meaning talking frankly (open, honest, direct). This can signify that the poet’s message is something serious/important.
    • From the title, we also learn that the poet uses personification, where non-humans are given human characteristics, in this case, turkeys that have the ability to talk.
    • A little bit of alliteration, as both Talking and Turkeys start with the same letter, T.
  • Structure
    • The poem is a free verse poem. It has four stanzas, with the first, second, third, and fourth stanza consisting of 16, 7, 8, and 8 lines/verses respectively. So, they are not of equal length. The rhyming also doesn’t really have a pattern.
  • Sounds
    • The rhythm of the poem is achieved through end (ex. Lines 33 & 35) and internal rhymes (ex. Line 7: “It could be yu mate, an not on your plate” and Line 34), repetition, which is used to emphasize the poet’s message (ex. Lines 9 & 13, Lines 17 & 18, and Lines 21 & 22).
  • Language
    • The language used is of course not proper English, instead it is shortened into “slang”, used comedically.
  • Mood
    • The mood is mostly comedic, but there are also some parts that are serious (ex. Lines 22 & 23).
  • Message
    • The poet wants to convey that turkeys should not be eaten and animals also have rights as he supports vegetarianism.
    • It is common tradition in the U.K. to eat turkeys during Christmas, and the poet wants to discourage this.
    • The poet wants to picture the turkeys as having their own minds to discourage people eating them.

So, that’s just a quick analysis. What do you think of the poem? In my opinion, it’s pretty good. It’s really creative and funny, but unfortunately I’m not going to let go of meat…yet?

The Concorde – Why Did it Fail?

Imagine a plane that can fly more than twice the speed of sound, travel across the Atlantic Ocean in only three and a half hours, and at the same time be a symbol of wealth and luxury. That is the Concorde.

From 1976 until 2003, the world had a way to cut travel times in half. Today if you want to travel from London to New York, it’ll take about 7 hours. What happened? What’s the Concorde?

The Concorde was a supersonic passenger aircraft jointly designed and built by the British and French. It had a top speed of more than twice the speed of sound (Mach 2.04) or 2,180 km/h. The program cost £1.3 billion ($3.5 billion), which is $20 billion today with 20 aircrafts built, including 6 non-commercial aircrafts. The Concorde mostly flew transatlantic flights, crossing the Atlantic Ocean. Why? This was because sonic booms caused when traveling supersonic would disturb people on the ground.

The “slender delta” platform and “droop-nose” in action.

The Concorde had a very iconic design. Due to its wing being a “slender delta” platform, the Concorde has a very high angle of attack during take-off and landing. This led to the iconic “droop-nose”, where they could lower the nose of the plane so the pilot could see out the cockpit.

So, many ask the question: What happened? Well there were many reasons, which we’re going to go through today.

First, there were costs. Flying supersonic is not cheap. The Concorde uses enormous amounts of fuel. During the early 70s, an oil crisis hit the world and oil prices skyrocketed. It was simply too expensive for most airlines to operate.

Look at how narrow the cabin is. The Concorde could only seat 120 passengers. Source: Wikipedia.

Second, the Concorde only had a capacity of 120 passengers, while planes like the Boeing 747 and Airbus A380 can seat over 400 passengers, even up to more than 800 passengers. Because of this limited capacity and the aforementioned development and oil costs, ticket prices could vary up to more than $10,000 for a return trip. That’s definitely not cheap, leading to the Concorde being a symbol of wealth and luxury.

Third, the Concorde had limited range. Although it could carry enough fuel to travel across the Atlantic, the Concorde could not travel farther distances like across the Pacific Ocean without refuelling.

Look at that sonic BOOM!

Fourth, as previously mentioned, the Concorde could only travel across the ocean because supersonic flights create extremely loud shockwaves when reaching and passing the speed of sound. This was the main obstacle for America’s development for a Boeing supersonic project. During tests conducted in Oklahoma City, citizens reported major damage to windows and noise disturbances. Therefore, the Concorde had to slow down and fly subsonic over land, undercutting the plane’s supersonic concept.

Because of this, less passengers found the Concorde useful enough to pay the hefty price tag. The Concorde had tough competition in the jumbo jet Boeing 747 that consumed much less fuel, had more seats, could fly much longer routes, and less expensive overall.

Air France Flight 4590

Finally, there was the tragedy of Air France Flight 4590. On July 25th, 2000, after only two minutes after takeoff from Charles de Gaulle airport in Paris en route to New York’s J.F.K. International Airport, the aircraft ran over debris that caused a blown tyre and a fuel tank puncture, causing the aircraft to crash into a nearby hotel. A total of 113 died that day, 109 aboard and 4 on the ground. This event quite severely damaged the Concorde’s reputation.

Eventually, the Concorde was leaking money and became a symbol of inefficiency. Newer planes were much cheaper to run and were more efficient. Fixing and building new Concordes would be wildly unprofitable. It seemed that the best way was to end it, let the Concorde land for good.

The Concorde’s last passenger service flight. Source: YouTube.

On April 10th, 2003, Air France and British Airways announced that the Concorde would be retired later in the year due to the Flight 4590 crash and the drop in the aviation market after 9/11. Air France had its last Concorde flight on June 27th, 2003 and British Airways retired its Concorde fleet on October 24th, 2003.

Many Concordes are now displayed in museums around the world. NASA has expressed plans for a quiet supersonic plane that may fly silently by 2022.

Sources/Bibliography:

  1. Edwards, P. (2016). This plane could cross the Atlantic in 3.5 hours. Why did it fail?. [online] Vox. Available at: https://www.vox.com/2016/7/19/12195452/concorde-supersonic-flight-fail [Accessed 24 Mar. 2019].
  2. Byers, A. (2003). The Crash of the Concorde. The Rosen Publishing Group.
  3. Cowell, A. (2003). Nostalgia Abounds as the Concorde’s End Is Set. The New York Times.

Saving the Blue Whale

(Disclaimer: I’m not a scientist/professor by any means, use the information here at your own risk lol! I just want to share and educate a little!)

Weekend Science! No more TGIF! It’s time to study! Every weekend, I’ll post something that’ll hopefully teach you something. Enjoy!

If we save our wild places, we will ultimately save ourselves.

Steve Irwin

Today’s topic is about how to save the blue whale. The blue whale is currently marked as endangered, though recovering. In today and next week’s edition of Sci-Fri, you will learn about the blue whale, why it is endangered, what we humans can do to help protect them, the advantages and disadvantages of the solution, and also the implications of the solution based on two factors (Economic and Environmental).

The Blue Whale (Balaenoptera Musculus)

What? – About the Blue Whale:

  • Kingdom: Animalia
  • Phylum: Chordata
  • Class: Mammalia
  • Order: Cetacea
  • Family: Balaenopteridae
  • Genus: Balaenoptera
  • Species: B. Musculus

Population: 10,000-25,000 (IUCN Status: Endangered)

Blue Whales (Balaenoptera musculus) are carnivorous marine mammals that live in all the world’s oceans except enclosed seas and the Arctic. Its size varies from 25 to 32 meters and it can weigh up to 200 tons. They are the largest animals known to have ever lived on the Earth. They look true blue underwater, however on the surface they look more of a mottled blue-grey.

Mottled: an irregular arrangement of spots or patches of colour.

Why? – Extinction Reasons:

Diagram 1. Blue whale population.
Source: Blue Whale Population v1.png, Peter Halasz (Blue_Whale_population,_Pengo.svg)
Year Global population Reference
Before whaling About 275,000 (Kemf & Phillips 1994)
1935 100,000 (Animal World 1972)
1962 930 – 2790 (IUCN 1966)
Late 1970s 4000 – 4500 (Burton & Pearson 1987)
1980 About 6500 (Nowak & Paradiso 1983)
1990 2500 – 3000 (Klinowska 1991)
2002 5000 (Pop 2002)

Table 1. Blue whale global population. Source: http://www.animalinfo.org/species/cetacean/balamusc.html

Picture 2. Blue whale ship strike death.jpg
  • Whaling: In the 20th century, whaling fleets killed about 360,000 blue whales in the Antarctic alone. Since then, the population has barely recovered, with the current population numbering between 10,000-25,0000 (Source: WWF).
  • Chemical and Sound Pollution: Pollution disturbs the navigation of blue whales and can even harm them.
  • Ship Strikes: Collisions with ships can cause bruises or even death for blue whales.
  • Overfishing of Krill: Krill is the blue whale’s only diet, and its overfishing can cause difficulty for blue whales when looking for food.
  • Climate Change: Global warming can cause blue whales to migrate during the summer to look for more food in colder climates. Because of this, blue whales may collide with ships or get stranded in coastal areas. Other problems caused by climate change that may damage blue whales include, but are not limited to, freshening of seawater, sea level rise, temperature changes, and ocean acidification.

How? – Solutions (5W+1H):

  • What is the solution?
    • Conserve blue whales by letting them live, grow, and reproduce safely so eventually the population can naturally recover to its original numbers.
  • How to save the blue whales?
    • The main problems that face blue whales right now are pollution, ship strikes, overfishing of krill, and most distressing of all, climate change.
      • Pollution: We have to make sure to properly dispose of harmful chemical substances because run-off may cause water pollution in the ocean. We can do this by taking our waste to a drop-off hazardous waste facility. We can also recycle our waste or take it to a place that will recycle it for you.
      • Climate Change: We can push for governments to make laws to reduce emissions of harmful gasses such as methane. We should also live a more eco-friendly life, one of the ways to do that being riding bicycles or driving electric/hybrid cars to reduce emissions. We can also invest in solar panels and conserve energy at home.
      • Whaling/Ship Strikes: We can support governments and organizations like WWF to create whale sanctuaries where whales can live and reproduce safely without the risk of ships strikes or commercial whaling.
  • Why should we save the blue whales?
    • One of the reasons why blue whales are very special is that it is the largest animal in the world. Therefore, it is important to preserve it for the next generation. Moreover, blue whales can also be a source of information and . discovery.
  • Who can help save the blue whale?
    • We can help fight against climate change and pollution by following the guide above while governments and organizations create whale sanctuaries.
  • When should we help the blue whale?
    • My proposed solution involves the blue whale population growing naturally, so it will take some time for their population to return to its original numbers. Because of this, it is best to start as soon as possible.
  • Where can we help the blue whale?
    • We can start at home, living an eco-friendly life while supporting and donating to organizations. We can also visit whale sanctuaries and take whale-watching tours to increase incentive to conserve blue whales.

Run-off: the draining away of water (or substances carried in it) from the surface of an area of land, a building or structure, etc.

Whale sanctuaries: Loosely used term, can mean areas of the ocean where commercial whaling is banned or a facility that houses or protects whales.

Advantages/Disadvantages:

  • Advantages:
    • Because the blue whale is the largest animal in the world, it is a very special creature and therefore is important to preserve.
    • They may also be useful for research.
    • Building whale sanctuaries can also help other marine animals, not only blue whales.
    • Whale sanctuaries can be made into tourist destinations as an incentive to build them and to finance them.
    • Whale watching tours are also popular and can be used to earn eco-tourism money.
  • Disadvantages:
    • Whale sanctuaries may cost a lot of money to build and maintain.
    • This solution will take a long time, and over the decades a problem may pop out that will slow down the recovery.

Implications:

  • Economic:
    • Although the investment in creating whale sanctuaries in the first place would be costly due to construction, maintenance, and many other factors involved in creating a facility this large. However, these whale sanctuaries can be made to earn eco-tourism money which will hopefully be enough to earn back the investment
  • Environmental:

Conclusion:

Sources/Bibliography:

  1. Blue Whale [Internet]. National Geographic. Available from: https://www.nationalgeographic.com/animals/mammals/b/blue-whale/ [Accessed 12 January 2019].
  2. Blue Whale [Internet]. WWF. Available from: http://wwf.panda.org/knowledge_hub/endangered_species/cetaceans/about/blue_whale/ [Accessed 12 January 2019].
  3. Elliott, W. and Simmonds, M. (2007). Whales in Hot Water? The Impact of a Changing Climate on Whales, Dolphins and Porpoises: A Call for Action. WWF-International, Gland Switzerland / WDCS, Chippenham, UK
  4. How to Save Endangered Whales [Internet]. Sciencing. Available from: https://sciencing.com/save-endangered-whales-2063162.html [Accessed 12 January 2019].
  5. Kemf, E. and Phillips, C. (1994). Whales in the Wild. Imprimerie Dupuis, World Wildlife Fund, Gland, Switzerland.
  6. Top 10 Things You Can Do about Climate Change [Internet]. David Suzuki Foundation. Available from: https://davidsuzuki.org/what-you-can-do/top-10-ways-can-stop-climate-change/ [Accessed 31 January 2019]
  7. Hazardous Waste [Internet]. BetterHealth. Available from: https://www.betterhealth.vic.gov.au/health/healthyliving/hazardous-waste [Accessed 31 January 2019]