Bitcoin is a decentralized digital currency introduced in 2008. Its value depends on market demand as it functions as a medium of exchange for goods and services. For something to be considered money, it must serve as a store of value, medium of exchange, and unit of account - however bitcoin is currently only a medium of exchange due to its highly volatile value. Bitcoins are produced through "mining", where users validate transactions by solving complex cryptographic puzzles. Successful miners are rewarded with newly minted bitcoins.

1. Math in the News
Issue 99

2. Before you start, click the money for a short video
summary!

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.  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. As you read, keep this question in mind…

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.  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.  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. 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. 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.  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: WeUseCoins.com)

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.  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.  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.  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.  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.  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.  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.  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.  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.  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. 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. Ana’s jacket will cost approximately 19.92
bitcoins.

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.  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 WeUseCoins.com and Bitcoin.org.