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Math in the News: Issue 99


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In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opoortunity to apply the concept of currency exchange.

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Math in the News: Issue 99

  1. 1. Math in the News Issue 99
  2. 2. Before you start, click the money for a short video summary!
  3. 3.  Development of Bitcoin ◦ In 2008, a paper written by Satoshi Nakamoto introduced to the world the idea of Bitcoin, a decentralized digital currency system ◦ In 2009, an exploit in an early bitcoin client allowed for the generation of large numbers of bitcoins.  An exploit is software, series of commands, or data set that takes advantage of a vulnerability in a system and allows for some an unintended or unexpected outcome, such as opening access to a computer system that allows for mass generation of bitcoins.
  4. 4.  Bitcoin is money, right? ◦ Generally, for something to qualify as money, it must be a store of value, a medium of exchange, and a unit of account. ◦ Bitcoin is a medium of exchange, as several business do accept bitcoins in exchange for goods and services. ◦ Bitcoin is not a store of value because currently, its value is highly volatile. ◦ Bitcoin is not a unit of account because, while some merchants allow people to buy with bitcoins, goods and services are not priced in bitcoins.
  5. 5. As you read, keep this question in mind…
  6. 6.  What are bitcoins? ◦ Bitcoins are digital coins you can send through the internet in exchange for goods and services  How do bitcoins get their value? ◦ Bitcoins value depends on the market. If enough consumers back bitcoins by believing in their value and using them for exchanges, then they inherently have value.  Basically, bitcoins have value if and because enough people both believe they have value and use them in exchange for goods and services.
  7. 7.  The Value of Bitcoin ◦ The conversion rate of bitcoins with other currencies is highly unstable ◦ In the United States, its dollar conversion rate has ranged between $0.30 and $1,135! ◦ One economist and investor posited that the value of one bitcoin will stabilize at a conversion rate of $40,000, while others suggest one bitcoin will be worth less than $10 or even reach a $0 value.
  8. 8.  The Value of Bitcoin cont… ◦ While bitcoin is highly unstable, developers devised a solution to manage inflation early on… ◦ Only 21 million bitcoins can be produced. Ever. ◦ There are currently 12 million bitcoins in circulation ◦ 25 new coins are produced roughly every 10 minutes.  Roughly every four years, the production rate will be cut in half.  It will take over 100 years to reach the cap.  Coins are produced through the mining process. Keep reading to learn about mining…
  9. 9. Consider the following The value of a dollar, euro, or pound is relatively stable. ◦ This will always be $1. ◦ This will always be €1. ◦ This will always be £20. ◦ The value of these currencies does fluctuate and inflate based on the market, but their value is fixed around the value that has been established over time and based on the physical note, bill, or coin that dictates its value.
  10. 10. Continue to consider the following… However ◦ This could be worth any amount of money because:  Contrary to pounds or dollars that have been around for decades and have an established value in the economy, the bitcoin is new, un-established, and untested by the market  Its physical form does not dictate its value Can you think of other reasons why bitcoin is less stable than other currencies?
  11. 11.  So, how does it work? ◦ First, one has to acquire bitcoins.  Individuals obtain a “wallet,” or a software that manages the bitcoins. The wallets are run by the internet, computer software, mobile phones, or hardware.  They can be bought and sold at various websites and are priced depending on current market value  Merchants can acquire bitcoins by accepting them in exchange for goods or services. ◦ Then, bitcoins can be used as currency wherever they are accepted.  Currently, over 12,000 businesses and charities accept bitcoin (Source:
  12. 12.  The Transaction ◦ The transfer of bitcoins is made directly between the two people involved in the transaction – the buyer and the seller  This means there is no third party, like a bank or merchant company, that needs to verify the transaction, has anything to gain from the transaction, or takes a portion of the buyer or seller’s money.  The open source, decentralized systems gets rid of the middle man and allows for open trade ◦ In order to ensure the security and validity of every transaction, Bitcoin uses mining
  13. 13.  Mining ◦ Mining is the basis behind the security of bitcoin ◦ Mining verifies bitcoin transactions, makes bitcoin incredibly difficult to hack, and keeps people from using the same bitcoin for multiple transactions ◦ Mining is also the way in which new bitcoins are issued Select the image for an overview on mining
  14. 14.  Miners ◦ Those who become miners are directly involved in both the security and production of bitcoins ◦ In order to become a miner, one needs specialized equipment and software and must be highly skilled in cryptography and programming.
  15. 15.  Mining the Transaction ◦ All transactions are stored in a ledger maintained by a central computer server ◦ Transactions are bundled into “blocks” and blocks are linked together on a block chain ◦ In order to make blocks, miners compete to break the cryptographic hash  A cryptographic hash is an output of a complex mathematical function which appears almost random and where the input is difficult to infer  Miners needs to solve for the cryptographic hash, whose length and difficulty is determined arbitrarily by the network
  16. 16.  Mining the Transaction cont… ◦ Miners race to solve the cryptographic hash ◦ Once a miner has solved the hash, the solution is sent out to other miners to confirm the result. It is much easier to confirm the solution of a hash than to find a solution.  Simple Example: The hash provided is 54. Miners need to find the two numbers the network is demanding that add to 54. This requires guess work and mathematical ability. A miner is notified by the network once they have correctly solved the cryptographic hash.  This example is easy, but the math and cryptography miners need to calculate is highly complex
  17. 17.  Mining the Transaction cont… ◦ A block is validated only after:  The cryptographic hash has been solved, and;  Miners have validated that no one bitcoin has been signed over to two different recipients, protecting against double spending ◦ Blocks are linked onto block chains ◦ Every block contains the cryptographic hash of the previous block. ◦ It is nearly impossible to modify a block once it has been solved because the blocks build on themselves
  18. 18.  Mining the Transaction ◦ Finally, once a block has been verified, the miner or pool of miners who solved it first receives 25 newly minted bitcoins  That is how new bitcoins are generated  As mentioned previously, the number of new bitcoins generated as the result of breaking a hash will halve every four years, gradually slowing the production rate of new bitcoins ◦ The bitcoin reward is an incentive to mining, driving people towards mining on their own or in pools ◦ The more miners, the more difficult it is for hackers to intercept, as they are competing with thousands of people who are constantly computing
  19. 19.  Mining the Transaction ◦ Mining secures transactions and the bitcoin network and initiates the minting of new bitcoins. ◦ The overall process of mining includes the following steps:  Transactions are gathered into a ledger and put into blocks  Miners validate transactions while computing the block’s cryptographic hash  The first successful miner(s) to solve the cryptographic hash send it to the network for validation and then…  That miner or miners obtain the next set of 25 newly minted bitcoins, which rewards their labor and brings new bitcoins into circulation
  20. 20.  So, now that we’ve looked at how Bitcoin works, let’s take it back to real world applications. On April 25, 2014, one bitcoin was worth: $466.51 €337.40 (euro) £277.62 (pound) Use this information to answer the following word problem… Source: Bitcoin Exchange Rate
  21. 21.  Ana wants to buy a Prada jacket on Overstock, one of Bitcoin’s authorized merchants. The jacket costs $9,294.90. How many bitcoins will the jacket cost?  We can use a proportion to solve this problem. First, what is the proportion? ◦ One bitcoin is to $466.51 as x bitcoins is to $9,294.90 1 bitcoin $466.51 = x $9,294.90
  22. 22. 1 bitcoin $466.51 = x $9,294.90 First, cross multiply 1 9,294.90 466.51x   Now, solve for x… 466.51 9,294.90x  Isolate x by dividing both sides by 466.51 466.51 9,294.90 466.51 466.51 x  19.92433173994127x 
  23. 23. Ana’s jacket will cost approximately 19.92 bitcoins.
  24. 24.  Here’s a word problem for you to try… ◦ Isaac just acquired 4 bitcoins. He lives in England and uses the pound (£) for currency. He plans to use the bitcoins to go shopping. He wants to buy the following:  Shoes for £56.99  Pants for £49.99  Belt for £69.99  Watch for £ 117.50  Hat for £39.99  How many bitcoins will Isaac spend?  How many bitcoins will Isaac have left after his shopping trip?
  25. 25.  Questions for Consideration ◦ What factors increase or decrease the value of bitcoins? ◦ Given that the maximum number of bitcoins that will ever be in circulation is 21 million (and currently there are only 12 million), what do you think is a practical dollar value for one bitcoin? ◦ What are the advantages and disadvantages of the Bitcoin currency system? Information provided on this issue of Math in the News is courtesy of and