Triangular Arbitrage is a strategy used in the foreign exchange markets in which there is a discrepancy between the exchange rates of three currencies and the trader seeks to take advantage of the discrepancy with no risk involved. This can be done when a trader places simultaneous trades to buy one currency and sell another, with both trades being conducted using a third currency.
With the $1 you purchase euros EUR/USD at an exchange rate of 1.2. This means for $1 you now have €0.83.
With the €0.83 you then purchase British pounds EUR/GBP at an exchange rate of 0.90. This means for €0.83 you now have £0.75.
With the £0.75 you then purchase U.S. dollars USD/GBP at an exchange rate of 0.72. This means for £0.75 you now have $1.04.
So from initially spending $1 you get back $1.04, this is a profit of $0.04.