Final answer:
President Theodore Roosevelt sent the Great White Fleet to demonstrate U.S. naval power and support American strategic interests, particularly in response to Japan's actions in Asia, as a part of his 'big stick' foreign policy.
Step-by-step explanation:
The president who demonstrated military might and sought to counteract the "yellow peril" by sending the Great White Fleet around the world was President Theodore Roosevelt. This action was part of Roosevelt's broader "big stick" foreign policy, which emphasized the use of military strength as a means of diplomacy without necessarily engaging in conflict. While President William McKinley was more cautious and focused on using America's industrial power to negotiate trade, engaging in some military skirmishes, Roosevelt believed in the proactive display of force to achieve foreign policy goals and to keep the peace.
Roosevelt's decision to send the fleet from December 1907 to February 1909 was also intended to send a clear message to Japan regarding American interests in Asia and reinforce the Open Door policy. The demonstration aimed to show that the U.S. Navy could project power globally and was introduced to the world as a goodwill tour. This impressive show of naval strength exhibited not only the capabilities of the U.S. Navy but also supported the strategic geopolitical interests of the United States.